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THE  EYE 
ITS   REFRACTION   AND    DISEASES 


•s^^' 


THE   EYE 


ITS  REFRACTION  AND  DISEASES 


THE  REFRACTION  AND  FUNCTIONAL  TESTING  OF  THE  EYE, 

COMPLETE  IN  ITSELF,  IN  TWENTY-EIGHT  CHAPTERS 

WITH    NUMEROUS   EXPLANATORY    CUTS 

AND   DIAGRAMS 


EDWARD   E.   GIBBONS,   M.D. 

ASSISTANT  SURGEON  OF  THE  PRESBYTERIAN    EYE,    EAR    AND    THROAT    HOSPITAL;     DEMONSTRATOR    AND  CHIEF  Ol 
CLINIC   OF   EYE  AND   EAR   DISEASES   IN  THE  UNIVERSITY  OF   MARYLAND,  BALTIMORE 


Neto  Yorit : 
THE   MACMILLAN   COMPANY 

LONDON  :   MACMILLAN  &  CO.,  Ltd. 
1904 


Copyright,  1904 
By  the  MACMILLAN  COMPANY 


Set  up,  electrotyped  and  printed  January,  1004 


PoEii  or 

1M(  NIW  IRA  PRINTIRO  OOHfUIIH 

.ANCAtTER,  PA. 


PREFACE. 


The  author  has  attempted  in  the  following  pages  to  supply  stu- 
dents of  ophthalmology  with  the  practical*  information  needed  upon 
the  various  subjects  treated. 

The  deductions  of  the  various  formulae  used  in  optics  have  been 
simplified  and  inserted.  It  is  customary  to  omit  the  mathematics  of 
the  subject  from  treatises  of  this  kind,  but  the  author  feels  that  the 
student  should  be  familiar  with  the  physics  involved  for  the  proper 
understanding  of  the  subject.  The  scope  of  the  work  precludes  as 
frequent  reference  to  authors  as  the  writer  would  like.  The  author 
feels  that  the  new  material  and  diagrams  the  work  contains  justifies 
its  publication,  so  offers  no  apology  for  adding  one  more  to  the 
numerous  books  upon  the  same  subject. 


TABLE  OF  CONTENTS. 

CHAPTER   I 
Light,  its  Propagation  and  Refraction i 

CHAPTER   n. 
The  Study  of  Refraction  by  Prisms  and  Lenses. 9 

CHAPTER   HI. 

Reflection  and   Image-Formation   by   Plane,  Concave  and  Convex 

Mirrors 47 

CHAPTER   IV. 

The  Gross  Anatomy  of  and  Physiology  of  the  Eye  and  the  Study 

OF  the  Theory  of  Gauss 56 

CHAPTER  V. 
Visual  Acuity  and  Accommodation 79 

CHAPTER   VI. 
Mechanism  of  Accommodation  and  Optical  Defects  of  the  Eye.  .     94 

CHAPTER  VII. 
Ophthalmoscopy  and  Oblique  Illumination 107 

CHAPTER  VIII. 
The  Appearance  of  the  Normal  Fundus  Oculi 133 

CHAPTER   IX. 

The  Study  of  the  Field  of  Vision 139 

vii 


Viii  TABLE   OF   CONTENTS. 

CHAPTER  X. 
The  Study  of  the  Color  Sense i6i 

CHAPTER  XI. 

The  Study  of  the  Light  Sense,  After  Images  and  Troxler  Phe- 
nomenon   *• 171 

CHAPTER  XII. 
Simulation  of  Blindness  and  Means  of  Detecting  It 177 

CHAPTER  XIII. 
Visual  Impressions 183 

CHAPTER  XIV. 
Entoptic  Phenomena 195 

CHAPTER  XV. 
Movements  of  the  Eyeballs.  . . ; 203 

CHAPTER  XVI. 
The  Study  of  the  Law  of  Listing ,      214 

CHAPTER   XVn. 
Normal  and  Abnormal  Refraction.     Hyperopia  and  Myopia 224 

CHAPTER   XVIII. 
Abnormal  Refraction  (continued).     Astigmatism.     Anisometropia.    241 

CHAPTER   XIX. 
Presbyopia 260 

CHAPTER   XX. 
Balance  and  Imbalance  of  the  Extraocular  Muscles  .    264 

CHAPTER   XXI. 
Manner  of  Detecting  and  Correcting  Errors  of  Refraction  ....   268 


TABLE    OF    CONTENTS.  IX 

CHAPTER   XXII. 
Optometers.     Prisoptometry.     Ridgeway's  Chromatic  Test.     Hotz' 

» 

Astigmatic  Test 308 

CHAPTER    XXIII. 
Ophthalmoscopy  in  Measuring  Errors  of  Refraction 331 

CHAPTER   XXIV. 
Retinoscopy 344 

CHAPTER   XXV. 
Ophthalmometry  and  Ophthalmophakometry 379 

CHAPTER    XXVI. 
Tests  for  Muscle  Imbalance , . . .  407 

CHAPTER   XXVII. 
Aphakia  and  Post-Operative  Refraction 435 

CHAPTER   XXVIII. 
Spectacle  and  Nose  Glass  Fitting  and  Neutralization  of  Lenses.  443 


THE  EYE,  ITS  REFRACTION  AND  DISEASES 


CHAPTER   I 

LIGHT,    ITS    PROPAGATION    AND    REFRACTION 

Light  is  that  which  renders  the  objects  of  the  external  world 
visible  to  us.  Light  emanates  from  all  luminous  and  illuminated 
bodies,  and  passes  in  every  direction  in  space.  It  travels  at  the  rate 
of  198,000  miles  a  second,  taking  about  eight  minutes  to  reach  us 
from  the  sun,  the  source  of  all  light.  Bodies  are  transparent  when 
they  transmit  light  to  the  extent  of  allowing  vision  through  them  ; 
translucent  when  they  allow  light  to  pass  through  them,  but  cannot 
be  seen  through.  Opaque  bodies  do  not  transmit  light.  Such  are 
wood  and  stone.  The  intensity  or  brightness  of  light  decreases  as 
the  distance  of  the  source  of  light  increases,  in  proportion  to  the 
square  of  the  distance  of  the  source  of  light.  Thus  at  three  feet 
away  the  brightness  of  a  light  is  one  ninth  of  what  it  is  at  one  foot. 
There  are  two  theories  as  to  the  nature  and  the  manner  of  propaga- 
tion of  light.  Either  theory  will  explain  all  the  phenomena  of  light 
concerned  in  the  study  of  optics.     The  theories  are  : 

1°.  The  Corpuscular  Theory,  as  considered  by  Newton,  is  that  light 
emanates  from  all  luminous  bodies,  and  consists  of  very  minute  par- 
ticles, too  small  and  subtle  to  exhibit  the  properties  of  ordinary  mat- 
ter, and  which  travel  in  straight  lines  and  produce  the  sensation  of 
sight  by  passing  into  the  eye,  and  striking  upon  the  end-organ  of  the 
nerve  of  sight,  the  retina. 

2°.  The  Undulatory  Theory,  or  Wave-theory  of  light.  According 
to  this  theory,  light  is  supposed  to  be  propagated  by  the  undulations 
of  a  subtle  ethereal  medium  that  pervades  all  space.     The  waves  of 


THE   EYE,   ITS   REFRACTION   AND    DISEASES. 


light  spread  from  center  to  circumference,  as  the  ripples  spread  in 
the  water  from  the  spot  where  a  pebble  has  dropped.  The  waves  of 
light  do  not,  however,  occupy  only  one  plane  as  the  ripples  of  water, 
but  pass  out  from  the  source  in  all  directions,  in  every  plane.  The 
cycle  at  the  origin  of  the  light  is  repeated  in  all  its  essentials  in  each 
surrounding  particle.  The  theory  that  light  travels  in  straight  lines, 
or  in  a  rectilinear  course,  is  not  at  variance  with  the  wave-theory  of 
light,  as  at  first  may  be  supposed.  The  direction  of  the  propagation 
of  light  is  as  if  it  traveled  as  the  arrow  flies.  A  chip  of  wood  on  the 
water  may  rise  and  fall  with  the  waves  but  its  course  will  be  straight 
ahead  with  the  current.  Undulations  of  light  are  perpendicular  to 
the  course  of  its  propagation,  or  ray.  We  know  that  light 
travels  in  straight  lines,  for  many  reasons.  The  one  reason 
that  will  appeal  to  us  all  is  our  inability  to  see  around 
corners.  And  if  we  look  at  an  object  through  a  long  nar- 
row tube  the  tube  must  be  turned  directly  towards  the 
object.  Again,  the  shape  of  the  shadows  cast  upon  the 
ground  by  the  sun  proves  that  light  has  a  straight  path. 
The  following  experiment  of  classical  interest  is  cited  as  a 
proof  of  the  wave-theory  of  light.  It  is  Young's  experiment. 
"Three  parallel  opaque  screens  are  placed  some  few 
inches  apart ;  in  the  first  is  made  a  narrow  slit,  or  opening 
with  straight  parallel  edges  (S);  in  the  second,  there  are 
made  two  slits  parallel  to  that  in  the  first  screen  (A 
and  B),  and  quite  close  together.  There  is  thus  a  narrow 
opaque  portion  between  A  and  B,  and  the  two  screens  are  so 
adjusted  that  when  a  source  of  light,  as  a  candle,  is  placed  in 
front  of  the  first  slit,  the  candle,  the  first  slit,  and  the  opaque  portion 
between  the  two  slits  are  in  the  same  straight  line.  The  two  slits 
are  now  equally  illuminated  by  the  slit  S,  but  there  will  not  be  uni- 
form illumination  over  the  third  screen,  which  is  receiving  light  from 
the  slits  A  and  B.  It  may  be  observed  that  on  this  third  screen 
there  are  bands,  parallel  to  the  slits.  That  is,  strips  of  the  screen 
are  illumined  while  the  screen  in  between  the  strips  remains  in  dark- 


LIGHT,   ITS    PROPAGATION   AND    REFRACTION.  3 

ness.  These  bands  will  be  at  fairly  equal  distances  apart.  It  may 
be  necessary  to  use  a  microscope  to  see  the  bands  clearly.  The 
only  satisfactory  explanation  of  this  phenomenon  is  as  follow :  the 
ether  waves  from  the  slit  S  reach  the  two  slits  A  and  B,  thus  mak- 
ing them  two  sources  of  waves,  which  are  identical  in  all  respects  if 
proper  precautions  are  observed.  The  two  sets  of  waves  that  pro- 
ceed from  the  slits  A  and  B  illuminate  the  third  screen  ;  but,  to 
reach  the  same  points  on  the  screen  the  two  trains  of  waves  must 
go  different  distances  in  general." 

The  waves  from  one  slit  in  the  second  screen  will  interfere  with 
the  waves  from  the  other  slit,  that  is  the  crest  of  one  wave  will  fall 
into  the  trough  of  another,  and  the  wave  will  be  broken  or  neutral- 
ized. The  disturbances  in  a  wave,  at  a  distance  apart  of  half  a  wave- 
length, are  exactly  opposite  to  each  other.  The  central  portion  of 
the  third  screen,  that  is  the  portion  in  line  with  the  slit  6"  and  the 
opaque  strip  between  the  slits  A  and  B,  will  be  illuminated  because 
the  two  trains  of  waves  reinforce  each  other ;  but  on  each  side  of 
this  bright  portion  there  will  be  a  series  of  points  such  as  described 
above,  where  the  difference  in  the  path  of  the  two  trains  is  I/2  (J 
being  a  wave-length,  or  the  distance  between  one  crest  and  the  next) 
and  there  is  darkness.  It  is  obvious  that  the  interference  bands,  as 
the  stripes  of  shade  on  the  third  screen,  between  the  light  bands, 
are  called,  are  not  a  phenomenon  of  light,  but  of  waves.*  Waves 
of  light  are  either  spherical  or  plane.  Spherical  when  the  wave-front 
is  curved  in  outline,  and  plane  when  the  wave-front  is  straight.  If 
the  spherical  wave  has  its  convexity  in  the  direction  of  propagation 
of  the  light  it  is  said  to  be  positive,  and  to  be  negative  if  the  con- 
vexity is  in  the  opposite  direction. 

The  arrow  heads  mark  the  direction  of  propagation  of  light.  Fig. 
A  represents  positive  spherical  waves,  Fig.  B,  plane  waves  and  Fig. 

*  Light,  electro-magnetic  and  sound  waves  are  similar  save  in  the  number  of  vibrations  per  second. 
If  the  waves  are  comparatively  few  in  number  they  are  perceived  as  sound  by  the  ear,  if  of  greater  fre- 
quency they  traverse  space  as  electro-magnetic  waves,  while  if  of  still  greater  frequency  they  call  forth 
sight.  In  many  particulars  light  and  electro-magnetic  waves  behave  alike,  which  has  given  rise  to  the 
so-called  electro-magnetic  theory  of  light. 


4  THE   EYE.   ITS   REFRACTION   AND   DISEASES. 

C,  negative  spherical  waves.  A  ray  of  light  is  the  direction  of  the 
propagation  of  the  light.  In  Fig.  A  the  rays  are  diverging,  in  Fig. 
B  parallel,  and  in  Fig.  C  converging.  A  number  of  diverging  rays 
are  spoken  of  as  a  pencil  of  light.  A  number  of  parallel  rays  com- 
pose a  beam  of  light. 
Waves  of  light  are  said  to 
be  positive  to  curved  sur- 
faces when  the  center  of 
curvature  of  the  surface 
and  that  of  the  waves  are 
on  opposite  sides  of  the  surface,  and  negative  when  on  the  saime  side. 

^  is  a  curved  surface  of  a  lens.  Waves  W  are  positive  to  it,  and 
waves  W ,  negative. 

There  are  two  remarkable  laws  of  light,  namely :  Refraction  and 
Reflection. 

Refraction. — Refraction  of  light  is  the  bending  or  alteration  in  the 
direction  of  a  ray,  when  it  passes  obliquely  from  one  medium,  or  sub- 
stance, into  another  of  different  density.  A 
wave  of  light  passing  through  the  air  con- 
tinues in  the  same  direction  until  it  meets 
with  some  obstruction  to  its  progress  at  the 
surface  of  a  denser  medium,  when  its  course 
is  changed,  its  ray  (course)  being  bent  to- 
wards the  perpendicular.  On  exit  from  the  denser  medium  the  ray 
is  deviated  from  the  perpendicular. 

A  Dioptric  Surface  is  a  surface  that  separates  transparent  or  re- 
fracting media  of  different  densities.  A  dioptric  medium  is  any  sub- 
stance that  can  be  seen  through.  From  8ta,  through,  and  oTrreLP,  to 
see. 

The  ray  of  light  that  impinges  upon  the  surface  of  the  refract- 
ing medium  is  the  incident  ray,  and  the  ray  at  its  exit  from  the  diop- 
tric medium,  the  refracted  ray. 

In  figure,  A  BCD  is  a  piece  of  glass.  Ray  10  is  incident  at  the 
point  O.     RR'  is  normal  to  the  surface  at  the  same  point.     The 


LIGHT,    ITS    PROPAGATION   AND    REFRACTION. 


angle  formed  by  the  incident  ray  and  the  perpendicular  to  the  sur- 
face at  the  point  of  incidence  is  called  the  angle  of  incidence;  such 
is  angle  I  OR'. 

If  the  ray  did  not  change  its  course  when  it  entered  the  refracting 
medium,  it  would  continue  on  the  path  Ox.     It  is,  however,  bent 
towards  the  perpendicular  RR',  and  occupies  a  path  along  00'. 
The  angle  between  the  perpendicular  and  the  refracted  ray  is  the 
migle  of  refraction.     If  the  ray   00'  continued  straight  on  as  it 
emerged  from  the  glass  it  would  occupy  the  path  O'x',  but  on  exit 
it  is  bent  from  the  perpendicular  to  the  surface  at  the  point  of  exit, 
and  takes  the  direction  O' K.     At  the  surfaces  of  the  medium  refrac- 
tion takes  place.     An  angle  of  incidence  and  of  refraction  are  formed 
at  each  surface  of  a  dioptric  me- 
dium.    If  the  sides  of   the   re- 
fracting medium  are  parallel,  as 
are  the  sides  AC  and  BD,  the 
ray  on  exit  is  parallel  to  the  ray 
on  entrance  ;  the  ray  is  therefore 
simply  displaced.    If  the  incident 
ray  is  perpendicular  to  the    re- 
fracting surface  it  passes  through 
the  medium  unrefracted,  as  LM.     The  reason  that  light  changes 
its  course  when  it  enters  a  medium  of  different  density  is  because 
the    medium    of  greater   density   offers    more   impediment   to   the 
progress  of  the  light.     The  denser  the  medium  the  slower  the  light 
travels  through   it.     Suppose    that  in   the  figure  above  the  cross 
lines  on  the  incident  ray,  which   represent  a  train  of  plane  light 
waves,  be  taken  to  represent  successive  columns  of  men,  marching 
side  by  side.     The  men  are  instructed  always  to  preserve  the  line. 
If  they  are  marching  in  the  direction  of  the  arrow-head,  those  on  the 
right  of  the  line  will  enter  the  obstruction  to  their  progress  first. 
They  will  not  be  able  to  proceed  so  fast,  and  in  order  that  the  line 
may  not  be  broken  the  men  on  the  left  of  the  column  will  wheel  to 
the  right.     After  all  the  men  are  in  they  progress  with  an  equal 


THE   EYE,   ITS   REFRACTION   AND    DISEASES. 


velocity.  On  exit  from  the  impediment  those  on  the  right  get  out 
first,  and  are  compelled  to  wheel  to  the  left  to  preserve  the  straight- 
ness  of  the  line.  The  relative  resistance  that  a  substance  offers  to 
the  passage  of  light  through  it,  as  compared  with  the  resistance 
offered  by  the  air,  is  called  its  index  of  refraction.  Air  is  taken  as 
the  standard,  and  its  value  to  be  one.  The  resistance  of  a  substance 
as  compared  with  that  of  a  vacuum  is  the  absolute  index  of  refraction. 
SnelVs  Law  is  that  the  sine  of  the  angle  of  incidence  is  to  the 
sine  of  the  angle  of  refraction  as  the  resistance  of  air  is  to  the 
resistance  offered  by  the  refracting  medium  to  the  passage  of  light. 

In  other  words  the  index  of  refrac- 
tion of  a  substance  is  the  sine  of  the 
angle  of  incidence  divided  by  the 
sine  of  the  angle  of  refraction.  The 
law  is  illustrated  in  the  following 
way : 

Let  y^  be  a  refracting  medium  ; 
abc  a  train  of  plane  waves  of  light, 
incident  to  the  surface  M.  The 
wave-front  d  would  advance  to  the  position  of  the  line  a'b\  if  every 
portion  of  the  wave  impinged  upon  the  surface  M  at  the  same  time. 
As  the  waves  form  an  angle  /'  with  the  surface  of  the  refracting 
medium,  the  retardation  in  the  wave-front  begins  below  and  ad- 
vances upwards.  This  causes  the  wave  to  assume  the  position  a'b" , 
after  refraction,  and  the  waves  pass  on  as  i,  2  and  3.  //'  =  angle 
of  incidence,  angles  /  and  /'  are  equal,  being  alternate.  Angle  R  = 
angle  of  refraction,  v  and  v'  are  radii  of  wave-fronts  or  rays,  v 
course  without  refraction,  v\  after  refraction.  Both  v  and  v'  may  be 
understood  to  mean  the  velocity  of  or  resistance  to  the  passage  of 
the  light  in  the  medium  B.  In  triangle  a'b' M^vja' M  =  ^\x\^  of  /, 
and  in  triangle  a'b"M,  v'la'M=  sine  of  R.  As  a'M  is  common  to 
both,  it  may  be  dropped  from  each,  then  sine  of  I  =  v,  and  sine  of 
R  =  v'. 


LIGHT,   ITS   PROPAGATION   AND   REFRACTION. 


Ergfo: 


sine  of  / 
sine  of  R 


V 

''v' 


Another  way  of  illustrating  Snell's  Law  is  by  the  following  diagram : 
CD  is  the  sine  of  the  angle  of  incidence,  and  Mx,  the  sine  of  the 
angle  of  refraction.  An  incident  ray  strikes  the  surface  6".  It  forms 
the  angle  of  incidence  DOC  with  the  normal  PP'  erected  at  the 
point  of  incidence,  with  the  surface  S.  The  angle  MOx  is  the 
angle  of  refraction,  formed  by  the  refracted  ray  and  the  normal  PP\ 
erected  at  the  point  O  perpendicular 
to  the  surface  S.  Draw  a  circle  around 
6>  as  a  center.  From  D  and  M  draw 
perpendiculars  to  the  line  PP' .  The 
sine  of  the  angle  COD  is  CDj  OD, 
and  the  sine  of  the  angle  MOx  is 
MxjMO.  Let  OD  and  MO,  radii 
of  the  circle,  be  equal  to  i . 

OD  and  MO  can  then  be  elimin- 
ated from  each  sine  fraction.  The 
index  of  refraction  of  the  medium,  whose  surface  is  S,  is  then 
CDj  Mx.  In  this  case  CD  is  taken  to  be  equal  to  4,  and  Mx,  3. 
Ergo  :  The  index  of  refraction  of  the  medium  is  4/3  or  1.33  times  that 
of  air.     The  indices  of  refraction  of  a  few  important  substances  are : 

Crown  Glass 1.5 

Flint  Glass 1.58  : 

Aqueous  humor 1-3365 

Cornea 1-3365  + 

Crystalline  lens 1.43 71 

Vitrous  humor 1-3363 

Water 1.33 

Practical  Demonstration  of  the  Refractio7i  of  Light. — Place  a  coin 
in  the  bottom  of  an  empty  vessel,  with  opaque  sides,  so  that  it  will 
just  be  hidden  from  your  view  by  the  side  of  vessel,  as  at  Cm  figure. 


8 


THE   EYE,  ITS   REFRACTION   AND  DISEASES. 


Fill  the  vessel  with  water  and  the  coin  will  become  visible  from  the 
same  position.     The  rays  of  light  that  pass  from  the  coin  towards 


the  eye  are  bent  at  the  surface  of  the  water  and  pass  into  the  eye, 

as  is  shown  in  figure.     The  coin  then  appears  to  be  on  the  line  C K. 

Place  a  stick  in  a  vessel  of  water.     The  stick  appears  bent  at  the 

surface  of  the  water,  causing  its  point  to  appear  nearer  the  surface. 


From  the  points  a,  b  and  c  rays  diverge.  Some  pass  up  as  i,  2,  and 
3  ;  others  enter  the  eye  E.  When  the  vessel  is  filled  with  water 
the  light  that  went  to  E  is  refracted  in  the  direction  of  x,  and  the 
light  that  went  up  as  i,  2,  and  3  is  refracted  to  the  eye  E.  The 
end  of  the  stick  as  well  as  each  point  in  it  beneath  the  surface  of  the 
water  appears  out  of  its  true  position.  The  end  C,  for  instance,  now 
appears  at  point  C 


CHAPTER  II 


PRISMS    AND    LENSES 


A  PORTION  of  glass  or  other  transparent  medium  with  plane 
(straight),  but  non-parallel  sides  is  called  a  prism.  Usually  the  sides 
of  the  prism  incline  towards  each  other  and  form  an  angle,  the  Re- 
fracting Angle  of  the  prism,  which  is  expressed  in  degrees.  The 
prism  may  be  cut  in  any  shape,  but  still  retains  its  properties  so  long 
as  its  sides  are  plane  and  non-parallel.  If  the  sides  are  parallel,  the 
medium  is  a  plane.  The  apex  of  the  prism  includes  the  refracting 
angle,  and  the  side  oppo- 
site the  apex  is  called  the 
base.  The  position  of  the 
prism  is  described  according 
to  the  direction  of  its  base. 
Thus :  Base  up  or  down 
to  the  right  or  left.  If  the 
prism  is  before  the  eye  and 
its  base  towards  the  nose,  we  speak  of  the  base  as  in  and  as  out 
when  the  base  is  next  to  the  temple. 

A  ray  of  light  entering  a  prism  emerges  deviated  towards  the  base 
of  the  prism.  The  ray  RO  would  continue  to  the  point  Q  if  refrac- 
tion did  not  occur  at  the  side  AB  of  the  prism.  The  right  ends  of 
the  wave-fronts  a,  b  and  c  enter  the  prism  first,  and  consequently  the 
ray  is  bent  towards  the  perpendicular  to  the  surface  at  the  point  of 
incidence.  The  ray  is  therefore  inclined  towards  the  base  of  the 
prism.  On  exit  the  wave-fronts  pass  out  of  the  prism  first  on  the 
left  end,  and  moving  faster  than  those  which  are  still  within  the 
prism,  cause  the  ray  to  be  inclined  again  towards  the  base  of  the 
prism.     In  the  figure,  i  is  the  angle  of  incidence  ;  2,  the  angle  of  re- 

9 


lO 


THE   EYE,  ITS    REFRACTION   AND   DISEASES. 


fraction,  and  3,  the  angle  of  deviation.  Angles  3  and  2  are  usually 
together  equal  to  angle  i.  In  weak  prisms  angle  3  is  equal  to  one 
half  of  angle  2.  If  an  object  be  looked  at  through  a  prism,  it  will 
appear  to  be  displaced  in  space  towards  the  thin  edge  or  apex  of  the 
prism.     The  light  appears  to  enter  the  eye  from  a  point  along  the 

ray,  as  it  emerges  from  the  prism,  the 
eye  not  taking  cognizance  of  the  fact 
that  the  light  has  twice  undergone  re- 
fraction at  the  surfaces  of  the  prism.  The 
)  eye  then  projects  the  object  (imagines 
it  to  be)  back  along  the  course  given  to 
the  ray  at  its  last  refraction.  When  a  prism  is  held  so  that  objects 
viewed  through  it  are  displaced  the  least,  the  prism  is  said  to  be  in 
the  position  of  minimum  deviation.  This  occurs  when  the  angle  of 
incidence  and  the  angle  of  emergence  are  equal.  The  angle  through 
which  a  ray  of  light  is  bent  in  refraction  is  called  the  Angle  of  Devi- 
ation. The  angle  of  deviation  may  be  described  as  the  angle  between 
the  direction  along  which  an  object  really  is  and  that  in  which  it  appears 
to  be,  when  looked  at  through  a  prism.  In  prisms  between  one  and 
ten  degrees  this  angle  is  one  half  the  refracting  angle  of  the  prism. 
In  the  figure  A  is  the  refracting  angle  of  the  prism,  /  the  incident 
ray,  E  the  ray  on  emergence,  i  the  incident  and  e  the  angle  of  emer- 
gence, D  the  angle  of  devi- 
ation, D  =^i  -\-  e  —  A,  for 
D  =  a'-\-b'  \  and  A=  180° 
—  x  =  c-{- c'.  The  deviation 
is  least  when  the  angle  of 
incidence  i,  is  equal  to  the 
angle  of  emergence  e  and 

the  course  of  the  ray  is  then  symmetrical  and  we  have  A  =  2c,  and 
D  =  2i—2c=  21  — A. 

By  Snell's  Law:  sin  z'/sin  r  =  z//z/',  in  which  vjv'  is  the  index  of 
refraction  of  the  prism.  Sin  i  =  vjv'  (sin  c).  We  can  replace  the 
sines  by  the  arcs  if  the  latter  are  small.     Ergo  : 


PRISMS   AND    LENSES.  II 

i  =  vjv'  [c],  and  D  =  ivjv'  -  A=  {v/v'  -  \)  A. 

If  the  prism  is  made  of  glass,  vjv'  ==  f  and  vfv'  —  \  =^. 

Therefore  D  =  ^A.  The  angle  of  deviation  produced  by  a 
prism  is  then  equal  to  one  half  of  the  angle  of  the  prism.  In 
stronger  prisms  the  amount  of  deviation  in  comparison  to  the  angle 
of  the  prism  rapidly  increases.  The  largest  possible  angle  that  an 
incident  ray  of  light  can  make  with  the  normal  to  a  refracting  sur- 
face, and  still  pass  out  of  the  medium,  is  called  the  Critical  Angle. 
A  ray  of  light  can  emerge  from  a  piece  of  glass  if  it  makes  an  inci- 
dent angle  equal  to  41°  48',  but  if  the  angle  of  incidence  is  greater 
than  this  the  ray  is  reflected  back  into  the  medium.  This  is  the 
limit  angle  of  refraction,  as  a  ray  cannot  be  bent  more  than  that 
on  entering  a  denser  medium.  The  critical  angle  from  water  to  air 
is  48°  35',  and  from  glass  to  air  41°  48'  (Ganot).  The  critical  angle 
is  designated  as  the  angle  of  incidence  that  corresponds  with  the 
angle  of  refraction  of  90°.  Total  refraction  takes  place  when  a  ray 
passing  through  a  dense  medium  meets  the  surface  separating  the 
denser  medium  from  a  rarer  one.  If  the 
angle  of  incidence  exceeds  the  critical  an-  j  j 

gle  all  the  light  is  reflected.    This  phenom-  jn'  |n' 

enon  is  spoken  of  as  Internal  Reflection,       __^t= —  ^  —):-^    — 
or  Total  reflection.     The  light  in  a  prism     —^-/\A^=^^''^T=^^^ 
may  suffer  a  number  of  reflections  at  the     ^^r=r'^^^^^^^:^^^^- 
surfaces   of   the  prism    and   then    finally 
pass  out.     In  this  way  a  prism  may  give  rise  to  multiple  images. 

/  represents  a  ray  that  makes  an  incident  angle  a  litde  less  than 
the  critical  angle  and  passes  out  of  the  medium  nearly  parallel  to  the 
surface.  /'  makes  an  angle  larger  than  the  critical  and  is  reflected 
back  into  the  medium,  at  the  surface  of  the  medium. 

Dip  a  pencil  into  a  glass  of  water,  and  we  will  see  it  mirrored 
from  the  surface  of  the  water,  if  we  look  at  the  surface  through  the 
side  of  the  glass,  from  below.  The  rays  of  light  that  pass  from  the 
points  of  the  pencil  in  the  water  pass  towards  the  surface  where 


12  THE   EYE,  ITS   REFRACTION   AND    DISEASES. 

they  undergo  reflection,  back  into  the  water  and  enter  the  eye  of  the 
observer.  The  surface  of  the  water  appears  as  a  silvered,  opaque 
surface,  there  being  no  ray  that  comes  from  above  reaching  the  eye 
as  all  are  refracted  towards  the  bottom  of  the  glass. 

The  most  useful  application  of  internal  reflection  is  in  the  rectan- 
gular prism.  Looking  perpendicularly  at  one  of  the  surfaces  we  see 
an  object  placed  in  front  of  the  other  face,  formed  by  total  reflection 
on  the  hypothenuse.  The  prism  need  not  be  rectangular  ;  a  prism 
of  60  degrees  gives  the  same  results,  but  the  three  faces  of  the  prism 
must  be  well  polished. 

This  principle  is  made  use  of  in  certain  optical  instruments. 

METHODS   OF   NUMERATING    PRISMS. 

I  °.  According  to  the  refracting  angle  of  the  prism.  Thus  a  prism 
that  includes  at  its  apex  an  angle  of  5  degrees  is  called  a  5°  prism. 
In  prisms  below  ten  degrees,  the  deviation  of  a  ray  passing  through 
them  is  equal  to  half  the  angle  of  the  prism,  but  for  prisms  above 
ten  degrees,  this  does  not  apply,  and  therefore  this  scale  of  numera- 
tion is  faulty. 

2°.  Dr.  Jackson  proposed  to  number  a  prism  according  to  the 
degrees  of  deviation,  and  to  replace  the  degree  mark  by  a  small  d, 
to  avoid  confusion,  thus:  Pr.  \d,  Pr.  2d,  etc.  The  unit  in  this 
Deviation  angle  system  is  about  double  that  of  the  Refracting-angle 
system. 

3°.  Den  net's  method  has  for  its  base  an  arc  called  a  radian,  whose 
length  is  equal  to  its  radius  of  curvature.  Such  an  arc  has  a  length 
of  57.295°.  A  prism  that  causes  a  deviation  in  a  ray  of  light  one 
one-hundredth  of  this  arc,  is  called  a  centrad,  and  denoted  thus  :  Pr. 
i^,  2^  and  so  on.  The  amount  of  deviation  of  one  centrad  is 
•57295°-  The  merit  of  this  system  is  its  uniformity,  ten  centrads 
having  ten  times  the  deviating  power  of  one  centrad, 

4°.  The  Prentice  or  Prism-diopter  Method.  The  standard  of  this 
method  is  a  prism  that  causes  a  deflection  of  i  cm.  in  a  ray  of  light 
at  a  distance  of  i  m.     By  this  method  it  is  easy  to  ascertain  the 


PRISMS   AND   LENSES.  1 3 

amount  of  prismatic  effect  in  a  decentered  lens,  by  multiplying  the 
strength  of  the  lens  by  the  number  of  centimeters  it  is  decentered. 
Thus  :  A  5-diopter  lens  decentered  i  cm.  would  cause  a  prismatic 
deviation  of  5  pr.  diopters  or  centrads  since  a  prism-diopter  and 
centrad  are  nearly  equal.  Their  relation  is  shown  in  the  figure 
(below).     Prism  diopters  are  denoted,  Pr.  i"^,  and  so  on. 

5°.  The  Meter-angle  System  of  Nagel.  Its  relation  to  the  meter- 
angle  of  convergence  will  be  seen  by  referring  to  the  latter  subject. 
The  meter  angle  is  the  angle  made  by  the  visual  axis  and  the  median 
plane  when  the  eye  fixes  an  object  on 
that  plane  at  i  m.  distant.  The  value  of 
the  angle  depends  of  course  upon  the  in- 
terocular  distance,  which  must  be  conven- 
tionalized when  used  for  the  purpose  of 
notation.  An  interocular  distance  of  .06 
makes  the  (one)  meter-angle  equal  to  3'^, 
being  about  the  average  interocular  dis- 
tance. The  advantage  of  this  system,  as  will  be  seen,  is  that  it 
corresponds  to  the  amount  of  convergence  as  well  as  the  amount  of 
accommodation  for  any  given  distance. 

Light  spreads,  as  we  have  seen,  divergingly  from  its  source ; 
therefore  all  the  rays  of  light  that  come  to  the  eye  are  divergent,  no 
matter  from  what  distance  they  come.  They  are,  however,  so  little 
divergent  when  they  reach  the  eye  from  a  distance  of  6  m.  or  twenty 
feet,  or  beyond,  that  we  in  practice  consider  them  parallel.  The 
nearer  the  eye  is  to  the  source  of  light  the  more  diverging  are  the 
rays  of  light  that  it  receives,  and  vice  versa.  If  a  circular  aperture 
one  centimeter  in  diameter  be  made  in  an  opaque  disc,  and  a  lumi- 
nous point  be  placed  at  varying  distances  from  it,  for  example  at  a 
distance  of  one  meter  and  at  ten  meters,  the  rays  of  light  coming 
from  ten  meters  passing  through  the  aperture  will  be  less  divergent 
than  those  that  come  from  a  meter.  A  cone  of  light  will  pass 
through  the  aperture  in  each  case,  but  the  shape  of  it  will  be  differ- 
ent according  to  the  distance  of  the  source  of  light  from  the  screen. 


14  THE   EYE,   ITS    REFRACTION   AND    DISEASES. 

When  the  round  hole  one  centimeter  in  diameter  is  at  a  distance  of 
one  meter  from  the  source  of  light,  the  cone  has  a  base  one  centi- 
meter in  diameter  and  the  apex  is  situated  in  the  luminous  source 
at  one  meter's  distance.  The  rays  have  diverged  i  cm.  in  traveling 
lOO  cm.  The  metal  disc  cuts  off  all  the  rays  having  a  greater  diver- 
gence. If  the  cone  of  light  passes  through  the  aperture  and  falls 
upon  a  distant  wall  the  cone  will  preserve  the  same  proportions,  that 
is  its  base  will  be  i/  loo  of  its  altitude.  If  the  point  of  light  is  at  a 
very  great  distance,  there  will  be  no  difference  in  the  size  of  the 
luminous  circle  and  the  size  of  the  aperture  in  the  screen  ;  the  rays 
therefore  have  practically  a  parallel  direction.  Rays  that  enter  the 
pupil  of  the  eye  from  a  distance  of  six  meters  have  so  little  diver- 
gence that  they  may  be  considered  parallel.  The  average  size  of  the 
pupil  is  4  mm.  ;  the  divergence  is  therefore  only  6/1000.  All  rays, 
diverging  more  widely  than  this  are  excluded  from  the  eye  by  the 
iris.  If  the  aperture  or  pupil  is  large,  then  infinite  distance  is  re- 
quired to  render  rays  parallel.  The  deviation  of  light  as  it  passes 
through  a  prism  depends  upon  several  conditions :  the  wave-number 
of  the  incident  light  (the  number  of  waves  in  a  second),  the  value 
of  the  angle  of  incidence,  the  material  of  which  the  prism  is  com- 
posed, and  the  size  of  its  refracting  angle.  The  greater  the  wave- 
number  (smaller  the  waves)  the  more  the  refraction  or  deviation  of 
the  light.  If  light  coming  from  a  source  that  appears  white  to  our 
eyes  is  made  to  pass  through  a  prism,  and  thrown  upon  a  screen, 
it  will  be  seen  that  the  area  of  illumination  on  the  screen  is  not  white 
but  colored.  The  colors  arrange  themselves  in  a  definite  order  and 
are  together  called  the  spectrum  ;  they  are  red,  yellow,  green  and 
blue  as  well  as  intermediate  shades.  White  light  is  considered  as  a 
mixture  of  the  waves  that  produce  these  separate  color  sensations. 
The  waves  that  produce  the  sensation  of  blue  m  our  eyes  are 
deviated  more  than  those  that  produce  red,  in  passing  through  the 
prism.*     The  number  of  waves  per  second  or  "  n,"  as  it  is  denoted, 

*  The  velocity  of  the  red  rays  is  the  greatest ;  they  are  therefore  retarded  the  least  in  passing  through 
the  dioptric  medium,  and  in  consequence  bent  least  from  their  course. 


PRISMS   AND    LENSES. 


15 


varies  from  45 1  million  millions  for  red  to  789  million  millions  for  violet. 
A  thermometer  placed  in  the  spectrum  will  register  a  higher  tem- 
perature as  it  is  moved  from  the  violet 
towards  the  red.  The  heating  effect  of 
the  sun's  ray  is  due  perhaps  to  the  red 
rays.  The  red  rays  have  the  greatest 
velocity. 

The  function  of  a  prism  of  breaking 
white  light  up  into  its  constituent  colors 
is  called  dispersion,  or  chromatic  aberra- 
tion. It  is  possible  to  make  two  prisms 
of  different  materials  and  refracting  angles,  so  that  when  they  are 
placed  side  by  side,  base  of  one  opposite  the  apex  of  the  other, 
the  dispersion  of  light  will  be  overcome  and  yet  the  refraction  of 
the  prism  not  destroyed.  White  light  then  in  passing  through  such 
a  prism  will  only  be  refracted.  Such  a  prism  is  called  an  achromatic 
prism. 

Light  enters  prism  A,  and  is  dispersed.  Then  entering  prism  B, 
the  light  is  condensed,  and  passes  out  of  the  prism  as  parallel  rays. 
Generally  the  medium  that  has  the  greater  index  of  refraction  has 
also  the  greater  dispersion,  but  the  two  are  not  proportional.  Flint 
glass,  for  example,  gives  a  dispersion  nearly  twice  that  of  crown 
glass,  while  its  index  is   1.7,  and  that  of  crown  glass   1.5.     In  the 

achromatic  prism  one  portion  is 
made  of  crown  glass,  and  the 
other,  whose  angle  is  about  half 
as  large,  is  made  of  flint.  A  prism 
of  flint  glass  produces  a  spectrum 
much  longer  than  one  of  crown 
glass.  Flint  glass  is  so  called  because  it  was  originally  made  from 
ground  flint.  It  is  the  sort  of  glass  used  for  optical  instruments  and 
table  ware,  and  contains  lead  as  an  ingredient.  Crown  glass  is  the 
common  window  glass,  and  contains  no  lead.  Its  refractive  power  is 
less  than  that  of  flint  glass. 


i6 


THE   EYE,   ITS   REFRACTION   AND    DISEASES. 


Crown   Glass 


Prism,  a  Vision  direct 


In  order  that  we  may  obtain  a  very  clear  spectrum  we  must  make 
use  of  a  very  narrow  slit,  through  which  the  light  passes  to  the 
prism,  and  interpose  a  lens  so  that  the  rays  of  each  color  may  be  re- 
united on  the  screen  in 
a  distinct  image  of  the 
slit.  The  spectrum  in 
reality  is  composed  of  a 
whole  series  of  images 
of  the  slit.  The  length  of  the  spectrum  depends  upon  the  size  of 
the  angle  of  the  prism  and  the  amount  of  its  dispersion. 

We  can  construct  a  series  of  prisms  that  possess  little  or  no  re- 
fraction, but  considerable  dispersion  ;  such  are  spoken  of  as  prism,  d 
msion  directe,  and  are  much  used  for  spectroscopes. 

A  Maddox  or  doubling  prism  is  an  obtuse  angle  prism,  and  is  to 
be  considered  as  two  prisms  placed  base  to  base.  Such  a  prism 
has  the  function  of  causing  an  object  seen  through 
it  to  appear  as  two. 

Lenses. — A  lens  is  a  transparent  medium  or  sub- 
stance bounded  by  at  least  one  curved  side.    Lenses 
are  divided  into  spherical  and  cylindrical  lenses.     Compound  lenses 
are  formed  by  the  combination  of  a  spherical  and  a  cylindrical  lens. 

A  spherical  lens  is  one  the  surface  of  which  is  equally  curved  in 
different  directions.  It  may  be  thought  of  as  a  section  of  a  sphere. 
A  cylindrical  lens  is  curved  in  one  direction,  and  in  the  direction  at 
right  angles  thereto  the  surface  is  plane  or  straight.  It  may  be  con- 
sidered as  a  surface  section  of  a  cylinder. 

Plano-convex.  —  One  side  plane  or 
straight  and  the  other  convex.      Most 


Maddox  Prism. 


Spherical 
Lenses. 


Convex,  positive  or  -f , 
converging  or  condens- 
ing lens.    Are  thicker  in  - 
the  center  than   on  the 
edge. 


spherical  spectacle  lenses  are  of  this 
variety. 

Bi-convex.  —  Double-convex,  both 
sides  are  convex. 

Concavo-convex. — One  surface  con- 
cave and  one  convex.  Convexity  in 
excess  of  concavity.  Positive  menis- 
cus or  periscopic  lens. 


PRISMS   AND    LENSES. 


17 


Spherical 
Lenses, 


Concave,  negative  or 
— ,  diverging  or  dispers- 
ing lens.  Concave  lenses 
are  thinner  in  the  center. 


Cylindrical  lenses 


Plano-concave. — One  side  plane,  the 
other  one  concave.  The  weaker  —. 
Spherical  spectacle  lenses  are  of  this 
variety. 

Bi-concave.  —  Both  sides  concave. 
Also  called  double-concave. 

Convexo-concave . — One  surface  con- 
cave and  the  other  convex,  the  con- 
cave surface  in  excess  of  the  convex. 
Negative,  or  minus,  meniscus,  or  per- 
iscopic  lens. 

Convex, 
Concave. 


spherical  Lenses. 


1  2 

Bi-convex- Piano-Curves. 

Cylindrical  Lenses- 


3  4  5  6 

Concavo-convex.    Convexo-conave.     Plano-concave.     Bi-concavc. 


Convex  cylincrical  Lens. 


Concave  cylindrical  Lens. 


Coquille.  Mi-coqulile. 


In  the  biconvex  lens  L,  E  is  its  edge  or  equator,  5"  and  S'  its  sides 
or  surfaces  ;  P  and  P' ,  the  central  points  of  these  surfaces,  called 
the  anterior  and  posterior  poles.  Point  O  is  the  geometrical  center 
of  the  figure,  and  is  called  the  optical  center.  C  and  C  are  the 
centers  of  curvatures  of  the  surfaces  of  the  lens.  A  line  passing 
through  the  anterior  pole,  the  optical  center  and  the  posterior  pole 


1 8  THE   EYE,   ITS    REFRACTION   AND    DISEASES. 

of  the  lens  is  called  the  principal  axis.     The  principal  axis  likewise 
passes  through  the  centers  of  curvature  of  the  lens.     This  line  is 

normal  to  the  surfaces  of  the  lens  at 
its  poles.  Any  other  ray  passing 
obliquely  through  the  optical  center 
of  the  lens  is  called  a  secondary  axis. 
All  rays  of  light  that  pass  through 
the  optical  center  of  a  lens  pass  out 
parallel  to  the  path  of  incidence,  but 
displaced  as  ray  AB'.  Convex  lenses 
act  upon  waves  of  light  that  pass 
through  them  as  two  prisms  placed  base  to  base.  The  rays  (lines  of 
propagation  of  the  light)  A  and  B  enter  the  lens  S.  Ray  A  strikes 
the  upper  prism  and  is  refracted  down  ;  ray  B  strikes  the  lower  one 
and  is  refracted  up.  The  two  rays  are  therefore  brought  together 
at  the  point  F.  The  point  to  which  waves  of  light  converge  after 
passing  through  a  convex  lens  is  called  a  focus  (real).  If  the  waves 
are  plane  waves  (parallel  rays)  they  are  brought  to  a  focus  at  a 
point  posterior  to  the  lens,  called  the  principal  focus,  and  a  vertical 
plane  through  this  point,  is  the  principal  focal  plane. 


A  Train  of  Plane  Waves  from  a  Distance  Entering  a  Biconvex  Lens. 


The  wave-fronts,  a,  b,  c,  d,  progress  with  equal  velocity  through- 
out their  length  until  they  reach  the  obstruction  offered  by  the  lens. 


PRISMS  AND    LENSES. 


19 


The  portion  of  the  wave-front  that  enters  the  lens  first  is  retarded  in 
its  progress  before  the  peripheral  portions.  The  waves  are  then 
caused  to  assume  the  form  within  the  lens,  as  shown  in  the  figure 
(^'  f^  Sy  ^^)-  O^  emerging  from  the  lens  the  waves  are  given  a  still 
greater  curvature  (as  i,  J,  k,  I),  converging  towards  F,  their  focus. 

The  distance  of  the  principal  focal  point  from  the  optical  center  of 
the  lens  is  called  the  focal  distance  or  focal  interval,  and  marks 
the  strength  of  the  lens.  There  are  two  systems  in  use  for  the  nu- 
meration of  lenses,  namely,  the  inch  and  the  metric  system.  The 
former  is  the  older  method  of  nomenclature.  According  to  this  sys- 
tem, a  lens  was  numbered  according  to  the  length  of  its  radius  of  cur- 
vature, assuming  that  its  index  of  refraction  was  1.5  (f).  A  double 
spherical  lens  of  such  an  index  has  a  focal  length  equal  to  its  radius 
of  curvature.  This  results  frogi  the  formula  F=RI 2{vlv'  —  i),  in 
which  F  stands  for  the  principal  focus,  R  for  the  radius  of  curva- 
ture, vjv'  for  the  index  of  refraction  of  the  glass  and  i  the  index  of 
air.  (See  the  deduction  of  this  formula.)  If  7?=  12,  vjv'  =  1.5,  the 
length  of  focus  will  h&  F  =  12/2(1.5  ~  i)=  12,  that  is,  the  focus  is 
equal  to  the  radius  of  curvature.  Glass  does  not  have  the  index  of 
1.5,  but,  according  to  Nagel,  varying  from  1.52  to  1.55,  and,  accord- 
ing to  Javal,  1.54.  If  we  substitute  the  last  value  in  the  formula,  we 
have^=  12/2(1.54—  i)=  ii.i,  that  is,  the  focal  length  is  less  than 
1 2  inches,  nearly  1 1  inches.  Again,  the  size  of  the  inch  varies  ac- 
cording to  its  nationality;  thus  the  English  inch  is  25.3  mm.;  the 
Austrian,  26.34  mm. ;  the  Prussian,  26.15  mm. ;  the  French  or  Paris 
inch,  27.07  mm.  Thus,  the  French  and  the  English  inch  differ  by 
^,  there  being  about  T^y  French  inches  to  40  English  inches.  In 
the  inch-system  a  lens  with  a  focal  distance  of  i  inch  is  taken  as  the 
standard.  The  stronger  the  lens  the  shorter  its  focal  distance  and 
vice  versa.  A  lens  whose  focal  distance  is  4  inches  is  \  as  strong 
as  the  lens  taken  as  the  standard,  and  is  called  therefore  a  :^-lens 
or  a  4-inch  lens.  Accordingly,  the  strength  of  a  lens  in  the  inch-sys- 
tem is  expressed  by  a  fraction,  the  numerator  of  which  is  i,  the 
standard,  and  the  denominator  the  focal  length  of  the  lens.     Thus  : 


20 


THE   EYE,  ITS   REFRACTION   AND    DISEASES. 


h  h  i>  ■§"'  ^^  ^  2-,  5",  6-  or  8-inch  lens.  When  the  metric  system  of 
mensuration  was  introduced  it  was  soon  adopted  by  Monoyer  in 
numbering  lenses.  In  the  metric  or  dioptric  system  a  lens  with  a 
focal  length  of  i  m.  is  taken  as  the  standard,  and  is  called  a  i  -diopter 
lens.  A  lens  that  has  a  focal  interval  of  20  cm.  is  five  times  stronger, 
and  is  called  a  5-D.  lens  (100-^20  =  5  D.).  Diopter  is  expressed 
by  the  letter  D,  and  we  combine  with  it  the  sign  of  the  lens  and 
its  kind  ;  thus,  a  +  2  D.  S.  (diopter  spherical),  a  —  2  D.  S.,  etc. 
Cylindrical  lenses  are  numbered  in  the  same  way ;  thus,  a  —  2  D.  C. 
(diopter  cylindrical).  As  a  diopter  is  equal  to  about  40  of  our 
inches  (accurately,  39.37)  it  is  easy  to  pass  from  one  system  to  the 
other,  by  dividing  the  known  strength  of  the  lens  in  one  system  into 
40.  Thus  :  Convert  the  following  lens  strengths  in  the  inch-system 
into  their  equivalents  in  the  metric  system  :  ^,  ^,  ^,  ^. 


Ans. 


2)40 


3)40 


5)40 


8)40 


20  D. 


I3  +  D- 


8D. 


5D. 


Express  the  equivalents  in  the  inch-system  of  the  following :  2  D., 
5  D.,  8  D. 


Ans. 


2)40 


5)40 


8)40 


20  m. 


Sin. ' 


5  in. 


or-^-.  i-  and  |-lens. 

If  the  source  of  light  is  nearer  the  lens  than  20  ft.  or  6  m.,  but 

beyond  the  principal  focus,  diverging  rays  (positive  waves  of  light) 

strike  the  lens,  and  are  brought  to  a 
focus  posterior  to  the  principal  focus. 
This  is  a  secondary  focus,  called  also 
the  posterior  conjugate  focus,  the 
source  of  the  light  being  the  anterior 
conjugate  focus.  The  conjugate  foci 
bear  the  relation  to  each  o.ther  that  if 

light  emanates  from  either  it  will  be  focused  at  the  other.     P  and  P' 

are  anterior  and  posterior  conjugate  foci  of  lens  ;  P  and  P,  anterior 

and  posterior  principal  focal  points. 


PRISMS  AND    LENSES. 


21 


If  the  light  emanates  from  a  position  closer  to  the  lens  than  the 
principal  focus,  it  is  not  brought  to  a  focus  at  all  on  emerging  from 
the  lens.  The  refracted  rays  are  rendered  relatively  convergent 
only ;  that  is  they  are  less  divergent  after  refraction  than  before. 

7^  is  the  principal  fo- 
cus of  lens  L;  a,  b  and 
c  are  diverging  rays 
of  the  incident  waves. 
They  are  rendered  less 
divergent  only,  taking 
the  paths  a',  b'  and  c' . 
Point  O  on  the  same 
side  of  the  lens  as  the 
source  of  light,  and  from  which  the  rays  of  light  appear  to  emanate 
after  refraction,  is  called  the  virtual  focus.  The  foci  mentioned 
before  have  been  real  foci.  Real  foci  are  those  produced  by  the 
actual  crossing  of  rays  of  light  after  refraction  and  can  be  caught  upon 
a  screen.  Virtual  foci  are  points  from  which  light  seems  to  proceed 
after  refraction.  They  cannot  be  caught  upon  a  screen  and  have 
an  existence  to  the  eye  of  an  observer  only.  Light  that  has  been 
rendered  convergent  by  a  convex  lens  is  rendered  more  so  by  a 
second  convex  lens.     We  have  then  the  third  law — that  converging 

rays  of  light  are  brought  to  a  focus, 
anterior  to  the  principal  focus. 

Rays  A,  B  and  Chave  been 
rendered  convergent  by  passing 
^  through  a  convex  lens.  Entering 
lens  L  they  are  rendered  more  so 
and  finally  caused  to  gather  about 
or  to  focus  at  the  point/!  F\s  the 
point  of  the  principal  focus.  AH  foci  other  than  principal  foci  are 
called  secondary.  The  following  laws  are  very  important  in  refrac- 
tion work,  and  should  be  studied  closely. 


22 


THE   EYE,   ITS   REFRACTION   AND   DISEASES. 


1.  Parallel  rays  of  light  are  brought  together  posterior  to  the 
lens  at  a  point  called  the  principal  focus.  Conversely  :  Light  that 
emanates  from  the  principal  focus  of  a  convex  lens  passes  from  the 
lens  parallel  or  plane. 

2.  Diverging  light  is  focused  posterior  to  the  principal  focus,  and 
the  more  diverging  the  further  posterior.  Conversely  :  Light  eman- 
ating from  a  point  further  from 
a  convex  lens  than  the  point  of 
principal  focus  passes  from  the 
lens  converging. 

3.  Converging  rays  of  light 
are  focused  anterior  to  the  prin- 
cipal focus.     Conversely  :  Light 

emanating  from  a  point  nearer  the  lens  than    the   principal   focal 

point  passes  from  the  lens  diverging. 

Rays  A  and  A  are  parallel  and  /^  their  focus. 
Rays  B  and  B'  are  divergent  and  f  their  focus. 
Rays  C  and  C  are  convergent  and  f  their  focus. 


CONCAVE    SPHERICAL    LENSES. 

Concave  spherical  lenses,  from  the  way  that  they  affect  light  pass- 
ing through  them,  may  be  regarded  as  composed  of  two  prisms, 
placed  apex  to  apex  at  the  center  of  the  lens.  Parallel  light  is 
rendered  divergent  by  passing  through  a  concave  spherical  lens. 
The  point  from  which  the  light  appears  to  emanate  after  refraction 
is  the  principal  focus  ;  it  is  situated  on  the  same  side  of  the  lens  as 
the  source  of  light,  as  are  all  foci  of  concave  lenses.  Rays  that  are 
divergent  on  incidence  are  rendered  more  so  by  concave  lenses,  and 
rays  that  are  convergent  are  rendered  less  so  by  passing  through  con- 
cave lenses.  Convex  lenses  shorten  focal  distances  and  concave  ones 
lengthen  them.  Rays  A  and  B,  entering  the  lens,  are  each  bent 
towards  the  base  of  the  prism. 


PRISMS  AND    LENSLIS. 


23 


Z  is  a  biconcave  spherical  lens  ;  P  and  P' ,  its  anterior  and  pos- 
terior poles  ;  O,  its  optical  center  ;  SS' ,  its  principal  axis  ;  C  and  C , 
the  centers  of  curvature  of  its  anterior  and  posterior  surfaces  respec- 
tively. Any  ray  that  passes  through  the  optical  center  but  not 
through  the  poles  of  the  lens  is  a  secondary  axis,  as  in  convex 
lenses.  R,  R  are  rays  or  radii  of  the  train  of  plane  waves  a,  b,  c,  d, 
incident  to  the  anterior  lens  surface.  In  passing  through  the  lens 
they  are  rendered  divergent,  that  is  the  waves  are  rendered  positive, 
as  A,  B,  C  and  D.  The  refracted  waves  seem  to  have  their  origin 
at  the  point  C,  from  which  they  appear  to  emanate.  CO  is  the  focal 
interval  of  L.     Concave  lenses  are  numbered  as  convex  ones  are. 


The  strength  of  a  lens  depends  upon  the  radius  of  its  curvature, 
its  thickness,  and  upon  the  index  of  refraction  of  the  substance  of 
which  it  is  made.  If  the  lens  is  made  of  ordinary  glass  its  focal 
length  nearly  corresponds  to  its  radius  of  curvature.  In  piano- 
spherical  lenses  the  focal  length  is  the  diameter  of  the  circle,  of  the 
circumference  of  which  the  curved  side  of  the  lens  forms  a  part.  If 
both  sides  of  the  lens  are  spherical  and  equally  curved,  the  focal 
length  is  equal  to  the  radius  of  a  circle,  of  the  circumference  of 
which  one  side  of  the  lens  is  an  arc  (if  the  index  of  refraction  of  the 
lens  be  considered  1.5).  If  we  represent  the  radius  of  curvature  of 
the  lens  by  R  and  the  index  of  the  glass  by  vj-j'  (the  ratio  between 
the  velocity  of  light  in  air  and  in  the  refracting  medium),  and  taking 
the  index  of  refraction  of  air  to  be  1 ,  we  have  the  following  formula 


24 


THE    EYE,   ITS    REFRACTION   AND    DISEASES. 


to  ascertain  the  focal  interval  of  a  double  convex  lens,  neglecting  its 
thickness:  F=  Rliivjv'  —  i),  ^ndF=RI{vlv'—i),  for  plano-convex 
lenses. 

The  method  of  obtaining  this  formula  is  as  follows :  Z  is  a  plano- 
convex spherical  lens,  x  being  its  plane  surface.  R  is  an  incident 
ray  of  light.  It  passes  unrefracted  to  0\  as  it  is  perpendicular  to 
the  plane  surface  of  the  lens.  00'  is  the  radius  of  curvature  of  the 
lens  side,  y.  O'R'  is  the  refracted  ray,  ergo  :  CO' R'  is  the  angle  of 
deviation  and  BGR'  the  angle  of  refraction.  Angle  RO'  O  is  the  an- 
gle of  incidence.  Angles 
RO'O  and  BO'R'  are 
proportional  to  their  sin  es. 
aa'  is  the  sine  of  angle 
RO'O,  and  <5<5' the  sine  of 
dangle  BO'R'.  Sides  ^(9' 
and  O'b  being  equal,  aa' 
is  inversely  proportional 
to  bb'  as  the  index  of  re- 
fraction of  the  lens  is  to  that  of  the  air.  Represent  the  index  of 
refraction  of  the  lens  by  vjv'  and  that  of  the  air  as  i,  and  we  have 
aa'  :bb':\  i  wlv'.  Angles  RO'O  and  BO'R',  being  small,  are  pro- 
portional to  their  sines:  RO' O  :  BO'R' waa' -.bb',  or  substituting 
RO'O-.BO'R'-.:  i :  v\v',  we  have  v\v'{RO' 0)  =  BO' R .  If  RO'O  is 
I  and  BO'R'  is  v\v',  the  angle  of  refraction  =  z//y  and  the  angle  of 
incidence  =  i .  The  angle  of  deviation  =  angle  of  refraction  —  the  an- 
gle of  incidence  =  vlv'  —  i . 

In  A  SO  a  and  SO'R';  A  RO'O  and  O'OS  are  equal  and  A  CO'R 
and  GR'S  are  equal.     The  side  6*  being  common  we  have  : 

O'OS-O'R'S-.'.R'S-.SO.     0'0S=i,  0'R'S=: /z/- i. 

0S=R  (radius).     SR'  =  F  (focal  length).     Ergo : 

I  iv/v'  —  I  ::  F :  R. 

R 


F= 


vjv'  —  I 


PRISMS  AND   LENSES. 


25 


The  focal  length  of  a  plano-convex  lens  is  equal  to  its  radius  of 
curvature  divided  by  the  index  of  refraction  of  the  lens  —  1 . 

In  the  double  convex  lens  the  lens  is  twice  as  strong  and  the  focal 
interval  half  as  long,  therefore  the  formula  is  : 


^=     ^ 


2{v/v'—  l) 


The  deduction  is  not  so  simple  if  the  lens  has  thickness.  In  the 
preceding  formula  it  was  supposed  that  the  lens  had  no  thickness  ; 
that  a  line  joining  its  centers  of  curvature  was  its  axis,  and  the  opti- 
cal center  of  the  lens  was  the  point  it  cut  in  passing  through  the 
lens.  If  the  lens  has  thickness,  we  must  suppose  that  the  focus  of 
*  the  first  surface  is  the  object  for  the  second  surface  and  take  into 
account  the  distance  between  the  surfaces. 

Let  us  designate  the  radii  of  curvature  of  the  two  surfaces  as  J^^ 
(for  the  first)  and  i?2  (^or  the  second). 

Incident  parallel  rays  to  the  first  surface  are  refracted  towards  the 
posterior  focus,  the  distance  of  which  is 

v/v'r      . 


vfi/  —  1 


As  this  point  is  behind  the  posterior  surface  it  is  considered  nega- 
tive.    In  the  formula  F^lf^-^-F^lfi^  i,/i  is  therefore  equal  to 


Fx  has  the  value  of 
and  F^  of 


v\v'  —  I  * 
vjv'  —  I 

^2 


v/v'  —  I  * 
Ergo : 

*  When  rays  pass  from  a  denser  into  a  rarer  medium  we  replace  vjz/  by  -p,  in  the  formulae. 


26  THE   EYE.  ITS   REFRACTION   AND    DISEASES. 

V 


-^'^^ 


F? 


V  V 

-  -  I      — ,  -  I 

V  V 
V 

■ 

or       ■  __  ^2  J Rt        _ 

I    +     D,  = 


a--')/^ 


R  R, 


\_(v  _    \R,  +  R,_(v         \(±.±\ 
f,      \v'      V     R,R^        \v'      'JKr.'^rJ' 

The  posterior  focus  is  then  deduced  by  the  following  formula 


F=te-0(i;+i)- 


This  answers  also  for  the  anterior  focus,  save  we  must  replace  Ri 
by  ^2.  and  vice  versa,  which  does  not  alter  the  expression  however. 

FORMATION    OF    IMAGES    BY    SPHERICAL    LENSES. 

If  a  convex  spherical  lens  be  placed  between  an  illuminated  object 
and  a  screen,  and  further  from  the  screen  than  its  principal  focus, 
there  will  be  formed  on  the  screen  an  image  of  the  object,  varying 
in  size  according  to  the  relative  position  of  the  object  and  the  screen 
in  regard  to  the  lens.  At  times  the  image  will  be  larger  than  the 
object,  and  at  times  smaller  as  the  screen  and  the  lens  are  moved 
closer  together  or  further  apart  and  their  distance  from  the  object 


PRISMS  AND    LENSES. 


27 


or 


changed.  The  image  will,  however,  always  be  upside  down 
inverted.  If  the  object  is  at  a  distance  from  the  lens  greater  than 
twice  the  focal  length  of  the  lens,  the  image  will  be  found  on  the 
opposite  side  of  the 
lens,  smaller  than  the 
object,  beyond  the 
principal  focus  and 
inverted. 

In  figure  let  L  be 
a  biconvex  spherical 
lens  ;  AB,  the  object ; 
OC,  greater  than  2/^  (twice  the  focal  interval).  Whatever  is  true  in 
-regard  to  the  two  points,  the  extremities  of  the  object,  is  true  of  all 
points  in  the  object  AB.  Draw  a  ray  from  each  extremity  of  the 
object  parallel  to  the  principal  axis  of  the  lens,  Cc.  These  two  rays 
will  be  focused  at  the  point  /^behind  the  lens,  the  principal  or  focus 
of  parallel  rays  of  light.  Now  draw  a  secondary  axis  to  the  lens 
from  each  end  of  the  object,  and  continue  the  lines  until  they  cross, 
behind  the  lens,  the  rays  from  the  corresponding  point  in  the  object. 
The  rays  coming  from  the  same  point  in  the  object  then  cross  behind 
the  lens,  those  from  above  cross  below  the  principal  axis  of  lens,  and 
those  from  below  cross  above  the  principal  axis.  The  points  a  and 
b  of  image  are  therefore  corresponding  points  to  A  and  B  of  the 
object.     The  image  is  therefore  inverted  and  smaller. 


2°.  The  converse  of  the  first  proposition  is  :  Object  at  a  distance 
less  than  twice  the  focal  distance  of  the  lens  but  beyond  the  principal 


28 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


focus.  In  this  case  the  image  is  on  the  opposite  side  of  the  lens, 
from  the  object,  inA  erted  and  real  (it  can  be  caught  upon  a  screen), 
larger  than  object,  and  further  from  the  lens  than  twice  its  focal 
length. 

F  on  each  side  of  the  lens  is  at  a  distance  (from  the  lens)  equal  to 
the  focal  distance  of  the  lens  L. 

2F  IS  at  twice  the  focal  distance.  Construct  figure  as  for  the 
previous  proposition. 

3°.  Object  at  a  distance  equal  to  twice  the  focal  length  of  the 
lens.  Image  is  on  the  opposite  side  of  lens,  inverted  and  of  the 
same  size  as  the  object,  and  at  the  same  distance  from  the  lens. 


2F 

F     ^~~^^-~~~ 

^  ^-^^^^"^~~^^>^'^^ 

2F 

0 

/ 

^^^-^^ 

O  is  object  and  i  the  image,  each  situated  at  twice  the  focal  dis- 
tance from  the  lens. 

4°.  Object  situated  at  the  principal  focus  of  the  lens.     There  is  in 
this  case  no  image  at  all,  as  the  rays  from  each  point  in  the  object 

emerge  from  the  lens  parallel,  and 
therefore  never  cross  to  form  foci. 
The  ray  from  point  A  of  object, 
parallel  to  the  primary  axis  of  the 
lens  L,  passes  through  F,  the  prin- 
cipal focus,  on  the  other  side  of  the 
lens,  but  after  refraction  it  and  the 
ray  from  the  same  point  formmg  a 
secondary  axis  to  the  lens  are  parallel.  So  are  all  other  rays  pro- 
ceeding from  a  common  point  in  the  object. 

5°.  If  the  object  is  nearer  the  lens  than  its  principal  focus,  the 
image  is  virtual,  erect,  larger  than  the  object  and  on  the  same  side 


PRISMS  AND    LENSES. 


29 


of  the  lens  as  the  object.  The  rays  from  the  head  of  the  arrow  after 
refraction  are  still  diverging.  Entering  the  eye  of  the  observer  they 
appear  to  have  started  from  the  point  a,  the  head  of  the  image. 
The  rays  of  light  from  the  ends  of  object  that  are  parallel  to  the 


>-.:- 


^\        ■^~. 

A~^~^--j 

/\ 

1                            F 

\.^ 

"~~~---^  F^.,.-^^^ 

0 

1                        ^^--B___^.^-l 

\v 

^^^ 

b'  tf: 


principal  axis  of  the  lens  are  still  focused  at  the  point  F.  Convex 
lenses  used  this  way  are  often  called  magnifying  lenses.  A  convex 
lens  used  as  a  magnifying  lens  is  also  called  a  simple  microscope. 

The  magnifying  power  of  any  optical  instrument  is  the  ratio  of  the 
apparent  size  of  the  image  to  that  of  the  object,  both  being  at  the 
distance  of  most  distinct  vision. 

The  magnification  of  a  convex  lens  is  greater  :  (i)  When  the  object 
is  placed  just  within  the  principal  focal  point  of  the  lens.  (2)  The 
stronger  the  lens  (the  shorter  the  focal  distance)  the  greater  the 
magnification.  (3)  As  the  observer's  distance  of  most  distinct  vision 
is  greater. 


__/ 

----..;--_--.____  f\                  ^ 

~~~               — ' 

Lllirnr^^     ^^^^^-^^^^ . 

h 

F 

^^:^^\u^^==^-=^ 

__-  '    f 

—\J 

In  figure  let  AB  be  the  object  and  A'B'  its  image  formed  at  the 
distance  of  most  distinct  vision,  a'b'  is  the  projection  of  AB  upon 
A'B'.     The   magnification  equals  A' OB' I  a' Ob',  or  A'B' I  a'b',  i.  e.. 


30 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


A'B'jAB.     In  the  triangles  A  OB'  and  AOB  which  are  similar, 
AB'\  AB:  '.DO:  CO. 

DO\s  the  distance  of  most  distinct  vision,  and  CO  is  nearly  equal 
to  FO,  ergo  :  the  magnification  equals  the  ratio  of  the  distance  of 
the  most  distinct  vision  to  the  focal  length  of  the  lens.  Let  x  be  the 
angular  magnitude  of  the  object  seen  by  the  naked  eye,  and  x'  the 
angular  magnitude  of  the  image  whether  real  or  virtual,  then  the 
magnification  is  x  -j-  x'.  This  rule  applies  to  telescopes.  The  mag- 
nification spoken  of  here  is  Hnear  magnification.  Superficial  mag- 
nification is  equal  to  the  square  of  the  linear  magnification  of  an  ob- 
ject.    The  magnifying  power  of  a  combination  of  lenses  is  equal  to 

the  multiple  of  the  magnifying 
power  of  each.  Thus  :  If  the 
objective  of  a  microscope  mag- 
nifies 20  times  and  the  eye- 
piece 10  times,  the  power  of 
the  microscope  is  equal  to  200. 
The  image  formed  on  the 
retina  of  the  eye  is  always 
smaller  than  the  object  and 
inverted,  because  the  object  is  always  situated  at  a  distance  from 
the  eye  greater  than  twice  the  focal  length  of  the  eyeball.  Con- 
cave spherical  lenses  form  erect,  virtual  images  on  the  same  side 
of  the  lens  as  the  object  and  smaller  than  the  object. 

Draw  lines  a  and  b  from  the  ends  of  the  object  O  through  the 
optical  center  of  the  lens.  Draw  a  ray  from  each  end  of  the  object 
to  the  lens,  parallel  to  the  principal  axis  PP,  and  call  them  a'  and  b'. 
The  rays  a'  and  b'  are  rendered  divergent  by  the  lens,  and  take  the 
course  of  a"  and  b"  after  refraction.  Project  the  rays  a"  and  b"  back- 
ward and  where  they  cross  the  rays  a  and  b  will  be  the  correspond- 
ing end  of  the  image  /.  The  relative  size  of  image  and  object 
are  to  each  other  as  their  distances  from  the  lens. 

In  figure  (on  opposite  page)  let  /,  be  a  convex  lens  ;  AB,  the  ob- 
ject, denoted  by  O  ;  ab,  the  image  denoted  by  i  ;   O' B  equal  to  D  ; 


PRISMS  AND    LENSES. 


31 


and  O'b  equal  to  d.  In  the  triangles  A  O'B  and  b  O'a,  we  have  the 
following  relation  of  sides. 

d:  D:\i:  O  or  df D  =  ij  O.  If  any  three  of  the  quantities  in  this 
proportion  are  known  the  other  one  is  easily  ascertained.  Ascer- 
tain the  distance  of  an  image 
from  the  lens  if  the  image  and 
the  object  are  of  the  same  size, 
and  the  object  at  100  cm.  from 
the  lens.  If  image  and  the 
object  are  of  the  same  size 
i\  O  =  I,  and  the  proportion  becomes  dj  {oo=  i,  ergo  :  d=  100  cm. 
Let  ^=  10;  2  =1  ;  and  0=  200.     Find  the  distance  of  the  object. 

loj D  =  1/200,  D  =  2000. 

If  the  focal  distance  of  the  lens  is  known,  we  have  the  following 
formula  to  ascertain  the  relative  distances  of  image  and  object.  In 
the  above  figure,  let  BO  =  D,  F' G  and  0'F=F;  BD  =  a  and 
Fb  =  b. 

In  triangles  ABD  and  DOB  on  one  side  and  GO'Fdind  Fba,  on 
the  other,  we  have  Oli  =  aj F=  Fjb,  or  ab  =  F'^;  which  can  also 
be  written  thus  :  Fl D-\- F\d=  i  or  iJ D+  i/d=  i/F,  or  i/d=  i/F 
—  ij D.  If  the  image  and  object  are  on  the  same  side  of  the  lens — 
that  is,  if  the  image  is  virtual  as  always  the  case  in  concave  lenses, 
ij  D  has  a  negative  value,  and  the  formula  is  written  thus : 

i/^=  ijF+iD. 

If  the  ratio  between  the  size  of  the  image  and  that  of  the  object  be- 
comes larger  when  the  position  of  the  object  in  regard  to  the  lens  is 
altered,  so  does  the  image,  and  vice  versa. 

In  both  convex  and  concave  lenses  the  image  and  the  object  move 
in  the  same  direction  when  the  position  of  either  is  changed,  that  is, 
when  the  object  is  moved  towards  the  lens ;  in  case  of  convex  lenses, 
the  image  recedes  further  from  the  lens  on  the  opposite  side.  In 
concave  lenses,  when  the  object  is  moved  nearer  the  lens,  the  image 


32 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


also  approaches  the  lens  on  the  same  side.  If  the  object  is  on  the 
left  of  the  lens  in  regard  to  the  observer,  when  it  is  moved  to  the 
right,  the  image  moves  to  the  right  in  both  cases.  This  is  the 
reverse  of  what  occurs  in  reflection. 


TO    ASCERTAIN    THE    STRENGTH    OF   A    LENS. 

If  the  lens  is  a  convex  one  an  image  of  a  distant  object,  one  fur- 
ther off  than  twenty  feet,  may  be  focused  on  a  screen  and  the  dis- 
tance of  the  lens  from  the  screen  measured.  In  case  of  concave 
lenses,  we  place  a  flame  a  great  distance  from  the  lens,  so  that  the 
virtual  image  of  the  flame  is  formed  at  the  principal  focus  of  the 
lens.  We  find  the  position  of  a  screen  placed  behind  the  lens,  so 
that  the  diffusion  or  luminous  circle  of  the  lens  has  a  diameter  equal 
to  twice  the  diameter  of  the  lens.  The  distance  of  the  lens  from  the 
screen  equals  the  focal  distance. 

The  reason  why  a  concave  lens  is  at  a  distance  from  a  screen 
equal  to  its  focal  distance  when  the  area  of  illumination  on  the  screen 

is  just  twice  the  diameter  of  the  lens, 
is  apparent  from  the  diagram. 

Let  Z,  be  a  concave  lens,  ab  the  ex- 
tent of  the  refracting  surface  ;  RR\ 
incident  rays  emerging  as  PP  ;  S, 
the  screen  and  cdthe  diameter  of  area 
of  illumination  and  /^principal  focus. 
We  are  to  prove  that  F0=  O  O',  when 
CD  =  2 ad.  Ca'  =  aO',  as  aO  =  a' 0\  ergo  :  aa'  =  Fo,  being  sides 
of  equal  angles,  with  equal  opposite  sides.     Therefore  F0=  00'. 

A  convex  lens  is  told  from  the  fact  that  if  an  object  is  looked  at 
through  the  lens  held  before  the  eye  and  the  lens  moved  to  the 
right  the  object  will  appear  to  move  in  the  opposite  direction,  to  the 
left  and  vice  versa.  The  apparent  motion  of  objects  viewed  through  a 
concave  lens  when  the  lens  is  moved  is  in  the  direction  that  the  lens  is 
moved.  The  reason  for  these  phenomena  is  that  the  lenses  act  like 
two  prisms.     As  long  as  the  light  reaches  the  eye  through  the  opti- 


PRISMS  AND    LENSES.  --> 

cal  center  of  the  lens  it  is  not  deviated,  and  its  apparent  corresponds 
with  its  true  course  ;  but  when  the  lens  is  moved  so  as  to  dislocate 
the  optical  center  to  one  side  or  the 
other  the  light  reaching  the  eye 
from  the  object  is  deviated  before 
entering  the  eye,  causing  it  to  ap- 
pear to  proceed  from  a  false  posi- 
tion in  space.  The  figures  above 
illustrate. 

In  the  figure  the  two  prisms  of  which  the  convex  lens  L  and  the 
concave  lens  L'  are  composed  are  shown.  The  ray  of  light  in  each 
case  is  bent  towards  the  base  of  the  prism  through  which  it  passes, 
Causing  the  object  along  a  to  appear  in  the  direction  of  a'.  The 
arrows  indicate  the  direction  the  lenses  have  been  moved  before  the 
eye.  Furthermore,  if  a  convex  lens  be  made  to  approach  the  eye, 
the  object  viewed  through  it  appears  to  recede,  and  vice  versa.  If 
the  lens  is  concave  the  object  and  the  lens  appear  to  move  in  the 
same  direction,  that  is,  when  the  lens  is  brought  nearer  to  the  eye 
the  object  seen  through  it  also  approaches  the  eye.  The  apparent 
motion  of  an  object  looked  at  through  a  spherical  lens  as  the  lens  is 
moved  backward  and  forward  before  the  eye  is  due  to  an  illusion. 
When  a  convex  lens  is  brought  nearer  to  the  eye  the  object  seen 
through  it  appears  to  diminish  in  size  as  its  retinal  image  decreases, 
which  causes  the  object  to  appear  to  recede.  The  opposite  is  the 
case  with  concave  lenses,  that  is,  when  they  are  brought  nearer  to 
the  eye  the  image  of  the  object  increases,  which  causes  the  object  to 
appear  to  approach.     (See  article  on  "  Optical  Illusions.") 

One  can  determine  the  radius  of  curvature  of  a  lens  by  applying 
the  formula  given  under  the  head  of  mirrors.  Knowing  the  radius 
and  the  focal  distance,  one  can,  from  the  following  formula,  ascertain 
the  index  of  refraction  of  a  lens  : 

ilF={vlv'-i)(ilR,+  ilR,), 

Rx  and  R^  being  the  radii  of  the  two  sides  respectively. 
3 


34 


THE   EYE.    ITS    REFRACTION   AND   DISEASES. 


Spherical  lenses  are  not  equally  refractive  throughout  their  sur- 
faces. Positive  spherical  lenses  are  usually  more  refractive  or 
stronger  near  the  equator  or  edge  than  at  the  center,  while  concave 
lenses  usually  have  the  opposite  defect,  of  being  stronger  at  the 
center.  This  unequal  refraction  in  different  portions  of  a  lens  is 
called  spherical  aberration.  It  is  said  to  be  positive  when  it  follows 
the  rule  in  convex  lenses,  and  negative  when  it  follows  the  rule  in 
concave  lenses.  A  positive  lens  at  times  possesses  negative  aberra- 
tion, and  vice  versa.  If  the  aperture  of  the  lens,  that  is,  the  angle 
formed  at  the  principal  focal  point  by  drawing  lines  from  the  edge 
of  the  lens,  does  not  exceed  ten  or  twelve  degrees  the  lens  is  free 
of  the  error  of  aberration.  The  degree  of  aberration  increases  as 
the  square  of  the  aperture  and  as  the  cube  of  the  refracting  power 
of  a  lens.  It  is  also  dependent  upon  the  distance  of  the  object  and 
the  form  of  the  lens.  A  plano-convex  lens  possesses  less  aberration 
than  a  biconvex  if  the  spherical  side  is  turned  towards  the  incident 
ray,  and  more  if  in  the  contrary  direction.  Spherical  aberration  in  a 
lens  may  be  overcome  by  placing  before  the  lens  a  diaphragm  with 
a  central  opening,  thus  excluding  light  from  entering  the  lens  save 
at  the  more  central  portions.  The  iris  of  the  eye  performs  this  func- 
tion. The  best  form  of  lens  is  what  is  called  a  crossed  or  periscopic 
lens,  in  which  the  radius  of  the  posterior  surface  is  about  six  times 
that  of  the  anterior.  The  refraction  at  1 5  mm.  from  the  center  of  sev- 
eral lenses  is  as  follows  :  each  has  at  the  center  a  strength  of  20  D. 


Crossed  lens, 


21. 1  D. 


Plano-convex  with 
convex  surface  in 
front, 

22,3  D 


Bi-convex, 


23.6  D. 


Plano-convex  with 
plane  surface  in 
front, 

23.8  D. 


Aberration  may  also  be  overcome  to  a  degree  by  combining  two 
lenses,  situated  at  a  little  distance  apart,  to  make  up  the  required 
strength  of  lens.  The  aperture  is  also  less,  and  it  is  not  necessary 
to  stop  a  great  part  of  the  lens,  thus  gaining  in  luminosity  of  the 


PRISMS  AND    LENSES.  -.r 

image.     The  error  of  aberration  increases,  pari  passu,  towards  the 
equator  of  the  lens. 

In  the  fig-lire  below,  the  rays  A,  B  and  C  are  brought  to  a  focus 
on  the  principal  axis  at  the  points  a,  b  and  c  respectively. 


It  will  be  noticed  that  the  convex  lens  is  stronger  nearer  the  edge 
and  the  concave  one  nearer  the  center.  The  areas  of  illumination 
produced  by  the  intersecting  of  refracted  rays  of  light  are  spoken 
of  as  Caustics  by  refraction.  There  are  produced  by  mirrors  Caus- 
tics by  reflection. 

Experiments  Demonstrating  Spherical  Aberration.  —  Take  a  plus 
20  D.S.  lens  and  upon  it  place  a  screen  with  four  openings  in  it, 


the  one  above  the  other,  along  the  diameter  of  the  lens.      Make  the 
apertures  in  the  screen  equidistant.     From  a  distant  luminous  point 


36  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

(a  small  circular  opening  in  an  opaque  lamp  shade)  receive  the  images 
upon  a  screen  held  behind  the  lens.  First  placing  the  screen  behind 
the  principal  focus  of  the  lens,  we  have  four  luminous  spots  corre- 
sponding to  the  apertures,  but  inverted.  The  two  central  points 
reproduce  the  form  of  the  source  of  light  enlarged,  but  the  periph- 
eral ones  are  elongated  in  the  horizontal  direction,  especially  if 
the  aberration  is  strong.  By  moving  the  screen  still  nearer,  the  two 
central  points  are  blended  into  one.  At  this  moment  the  screen  is 
at  the  focal  distance  of  the  central  part  of  the  lens,  but  still  beyond 
the  peripheral  foci.  By  altering  the  position  of  the  screen  behind 
the  lens  all  the  phases  shown  in  the  figure  can  be  observed. 

Where  the  rays  from  several  holes  in  the  screen  on  the  lens  cross, 
there  will  be  produced  only  one  point  of  illumination.  Reference  to 
the  figure  will  explain.  The  vertical  dotted  lines  represent  the  dif- 
ferent positions  of  the  screen ;  the  dots  on  the  Hnes,  the  number  and 
form  of  the  illuminated  areas  in  the  different  positions  of  the  screen. 

All  four  images  of  a  candle-flame  produced  through  the  openings 
I,  2,  3  and  4  in  the  screen  over  the  lens  can  not  be  brought  into 
good  focus  in  any  one  position  of  the  screen  placed  to  receive  them, 
behind  the  lens.  The  images  produced  through  the  central  open- 
ings are  well  defined  at  a  point  further  from  th,e  lens  than  those 
through  the  peripheral  openings,  showing  the  lens  to  be  weaker 
nearer  the  center  than  on  the  edge.  If  we  hold  a  strong  convex 
lens  nearer  a  screen  than  its  principal  focus,  the  image  of  a  luminous 
point  is  a  diffusion  circle,  the  edge  of  the  circle  being  brighter  than  the 
center,  while  if  the  screen  is  beyond  the  point  of  the  principal  focus 
the  diffusion  circle  is  brighter  in  the  center.  (A  diffusion  circle  is 
the  circular  area  of  illumination  on  a  screen  produced  by  a  point  of 
light  out  of  focus.)  In  figure  above  we  see  that  the  rays  of  light 
passing  through  the  convex  lens  are  condensed  towards  the  border, 
between  the  lens  and  the  focus  and  towards  the  center,  beyond  the 
focus.  We  can  also  gain  some  evidence  of  spherical  aberration  by 
the  study  of  the  shadows  cast  through  lenses.  Hold  a  convex  lens 
of  about  twenty  diopters  in  front  of  a  screen  beyond  its  principal 


PRISMS  AND   LENSES. 


37 


focus.  Place  a  hat-pin  against  the  lens.  It  will  be  noticed  that  the 
shadow  of  the  pin  cast  through  the  lens  on  the  screen  is  only  straight 
when  the  pin  coincides  with  the  axis  of  the  lens.  Otherwise  it  will 
be  curved  with  its  convexity  towards  the  center  of  the  diffusion  circle 
cast  on  the  screen.  If  the  lens  is  held  closer  to  the  screen  than  its 
principal  focus,  the  shadows  will  have  their  concavities  towards  the 
center  of  the  diffusion  circle,  but  the  curve  is  not  so  pronounced  as 
before.  By  referring  to  the  figure  illustrating  the  error  of  aberra- 
tion on  the  preceding  page,  it  will  be  noticed  that  the  circles  of  diffu- 
sion increase  in  widths  towards  the  periphery,  when  the  screen  is 
beyond  the  principal  focus,  and  diminish  towards  the  periphery  when 
the  screen  is  nearer  the  lens  than  the  principal  focus. 

No.  I  represents  the  lens  divided  into  equal  concentric  circles, 
with  the  pin  across  its  surface.  No.  2  represents  the  circles  of  dif- 
fusion between  the  lens  and  its  principal  focus  and  as 
the  zones  become  narrower  towards  the  edge,  a'  is 
relatively  nearer  the  center  than  b',  which  gives  the 
shadow  its  particular  curved  form.  No.  3  represents 
the  circles  of  diffusion,  and  the  shadows,  when  the  lens 
is  beyond  its  focus  [a!  relatively  further  from  the  cen- 
ter than  b'). 

Knowing  the  position  of  the  concentric  circles  of 
the  diffusion  spots,  it  is  easy  to  construct  the  form 
of  the  shadow,  since  the  shadow  of  the  point  of  the 
pin  must  be  at  the  same  angular  distance  from  the 
center  as  the  point  of  the  pin  itself.  A  lens  with  the 
reversed  kind  of  aberration,  that  is  an  overcorrected 
lens,  will  show  the  reversed  phenomenon,  while  an 
aplanatic  one  will  not  show  any  curving  of  the  shad- 
ows. As  all  spherical  lenses  act  upon  light  that 
passes  through  them  as  two  prisms  in  the  bending  of  the  light, 
they  likewise  act  as  prisms  in  the  dispersion  of  the  light ;  hence  all 
lenses  possess  the  error  of  chromatic  aberration.     This  error  or  defect 


38  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

is  of  small  extent  in  lenses  of  the  size  that  are  used  in  refraction 
work,  but  in  optical  instruments  where  great  accuracy  and  detail  of 
images  is  needed  it  interferes  very  much.  This  evil  can  be  over- 
come in  a  great  measure  by  combining  with  the  convex  lens  a  con- 
cave lens  having  a  different  index  of  refraction,  in  the  same  manner 
as  chromatic  aberration  is  overcome  in  prisms.  The  convex  lens  is 
usually  made  of  crown  glass,  and  the  concave  one  of  flint  glass. 
Such  a  lens  is  called  an  achromatic  lens.  Chromatic  aberration  is 
overcome  to  a  great  extent  in  the  eye  by  the  superficial  layers  of  the 
crystalline  lens  having  different  indices  of  refraction,  and  also  by  the 
combination  formed  by  the  biconvex  crystalline  lens  and  the  concavo- 
convex  vitreous  body,  having  an  index  of  refraction  differing  from 
that  of  the  lens.  The  human  eye,  however,  is  not  entirely  free  of 
chromatic  aberration.  It  has  been  variously  estimated  to  be  from 
1.3  D.  to  as  much  as  3  D.  Helmholtz  gives  as  an  average  1.8  D. 
The  dispersion  of  the  eye  is  a  little  greater  than  it  would  be  if  filled 
with  water.  By  passing  through  a  lens,  the  colored  rays  are  sepa- 
rated, the  violet  rays  being  refracted  to  a  greater  extent  than  the  red 
rays,  and  hence  the  focus  of  the  former  is  nearer  to  the  lens.  This 
is  the  reason  that  the  image  formed  by  a  convex  lens  is  bordered 
with  red  inside  the  focus  and  with  blue  when  beyon^  the  focus.  The 
image  of  an  achromatic  lens  no  longer  presents  red  and  blue  borders, 
but  there  are  often  traces  of  green  and  purple.  By  combining 
several  glasses  of  different  kinds  these  colors  can  be  made  to  disap- 
pear as  shown  by  Zeiss. 

The  chromatism  of  the  eye  can  be  demonstrated  by  the  experi- 
ment of  Wollaston.  A  luminous  point  seen  through  a  prism  gives 
a  linear  spectrum,  but  it  is  observed  that  we  cannot  see  distinctly  the 
red  and  the  violet  end  of  the  spectrum  at  one  and  the  same  time. 
If  the  eye  is  normal  in  regard  to  the  way  it  acts  upon  the  light  enter- 
ing it,  or  emmetropic  as  such  a  condition  is  spoken  of,  and  the  lumi- 
nous point  at  a  distance  of  twenty  feet  or  more,  the  red  end  of  the 
spectrum  will  appear  as  a  narrow  line,  while  the  violet  end  will  be 
drawn  out  into  a  wide  band  and  will  often  appear  to  be  divided. 


PRISMS  AND    LENSES.  39 

If  the  observer  goes  nearer,  taking  care  not  to  accommodate  or 
adjust  the  eye  for  the  violet  extremity,  he  finds  a  place  where  his  eye 
is  adjusted  for  the  violet  end  of  the  spectrum,  while  the  red  end  is 
in  turn  diffuse.  The  observer  can  therefore  determine  his  far-point 
(the  distant  point  for  which  the  eye  is  adjusted  when  at  rest)  for 
each  end  of  the  spectrum  ;  the  difference  gives  the  degree  of  chro- 
matic aberration.  Fraunhofer  determined  the  distance  at  which  he 
could  see  a  spider's  web  suspended  in  red  and  in  blue  light,  and 
finding  that  the  distance  differed,  arrived  at  some  very  accurate 
resVilts.  The  chromatic  aberration  of  the  eye  increases  as  the  pupil 
is  dilated,  so  it  is  well  to  dilate  the  pupil  when  studying  it.  We 
could  correct  the  chromatic  aberration  of  the  eye  with  a  concave  lens 
of  flint,  exactly  as  we  correct  the  chromatic  aberration  of  a  convex 
lens  made  of  crown  glass.  The  dispersion  of  flint  glass  is  about 
three  times  that  of  the  eye.  As  the  refracting  power  of  the  eye  is 
about  60  D.,  a  concave  flint  glass  of  about  20  D.  would  be  needed 
to  correct  the  aberration.  A  myope,  then,  of  20  D.  would  have 
at  the  same  time  his  myopia  and  his  chromatic  aberration  cor- 
rected. An  emmetropic  eye  would  need  in  addition  to  this  a  con- 
vex achromatic  lens  of  20  D.  to  remain  emmetropic.  Such  glass 
has  not  been  found  to  increase  the  visual  acuity  to  any  marked 
degree. 

The  eye  free  of  spherical  aberration  sees  a  circle  of  light  of  uniform 
brightness,  while  if  the  center  appears  more  luminous  there  is  present 
aberration  (positive).  The  edge  will  appear  more  luminous  if  the 
aberration  is  overcorrected,  or  negative,  or  if  the  luminous  point  is 
within  the  far-point.  If  one  looks  at  a  circle  of  light  through  a  con- 
vex lens  strong  enough  to  render  the  eye  myopic  and  to  cause  the 
luminous  source  to  appear  as  a  circle  of  diffusion,  and  holds  a  hat-pin 
in  front  of  the  eye,  the  shadow  of  the  pin  is  seen  in  ordinary  aberra- 
tion, with  its  concavity  towards  the  periphery.  If  the  concavity  is 
towards  the  center  the  aberration  is  overcorrected.  Upon  this  prin- 
ciple Dr.  Tscherning  constructed  the  little  instrument  called  Aberro- 
scope.     It  consists  of  a  plano-convex  lens  on  the  plane  side  of  which 


40  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

is  a  series  of  lines  dividing  the  space  into  little  squares.  The  instru- 
ment is  held  I o  or  20  cm.  in  front  of  the  eye,  to  observe  whether  the 
lines  appear  curved  or  not.  Young's  optometer  enables  us  to  meas- 
ure the  amount  of  aberration  of  the  eye  directly.  The  optometer  has 
the  form  of  a  little  rule.  On  one  side  is  drawn  a  fine  white  line  on  a 
black  background.  We  look  along  this  line  through  a  lens  of  plus 
10  D.  In  front  of  the  lens  moves  a  small  horizontal  rule  in  which 
are  different  groups  of  slits. 

Placing  the  two  slits  that  are  in  the  middle  of  the  slide  in  front  of 
the  lens,  causes  the  white  line  on  the  rule  to  appear  doubled,  except 
where  the  line  is  seen  distinctly.  If  the  E.  is  not  using  his  accommo- 
dation, the  lines  will  appear  to  intersect  at  the 
far  point  of  the  objective  lens  or  at  10  cm. 
from  the  eye.  To  measure  the  refraction  the 
distance  between  the  point  where  the  lines  intersect  and  the  lens  is 
measured  in  cm.  and  divided  into  100  cm.  to  obtain  the  refraction  in 
diopters.  We  can  determine  the  near  point  of  accommodation  in  the 
same  manner  {g.  v. ),  The  other  groups  of  slits  are  used  to  measure 
the  refraction  in  different  parts  of  the  pupillary  area,  or 
the  square  opening  and  the  slide  b,  used.  By  lowering 
the  rule  "  (5 "  more  or  less  in  front  of  the  eye  more  or  less 
of  the  center  of  the  pupillary  space  is  excluded  from  the 
visual  act.  The  difference  in  the  refraction  between  the 
central  and  the  peripheral  parts  of  the  pupil  gives  the 
amount  of  spherical  aberration  resident  in  the  eye.  By 
rotating  the  instrument  around  its  longitudinal  axis  the 
refraction  can  be  measured  in  different  meridians,  and  thus  astio-ma- 
tism  detected.  In  this  manner  Thomas  Young  detected  astigma- 
tism in  his  own  eyes. 

Cylindrical  lenses  are  either  convex  or  concave.  A  convex  cylin- 
drical lens  may  be  thought  of  as  a  vertical  surface-section  of  a  cylin- 
der of  glass,  and  a  concave  cylinder  as  a  section  of  the  mould  in 
which  the  +  cylinder  was  formed.  A  cylindrical  that  at  right  angles 
to  its   length  and  plane   or  lens  like  the  cylinder  is  curved  in  one 


PRISMS  AND   LENSES. 


4.1 


direction,  straight  in  the  direction  of  its  axis.  A  line  passing 
through  the  middle  of  the  lens  parallel  to  its  plane  sides  is  called 
the  axis  of  the  cylinder. 

abed  is  a  cylinder,     aef-cgh,  a  surface  section,  or  a  convex  cylindri- 
cal lens,  and  ijlk-mnop,  a  concave  cylindrical  lens  of  the  same  strength. 

Waves  of  light  that  enter  the  cylindrical  lens  par- 
allel to  its  axis  pass  through  unrefracted.  Waves 
that  enter  at  right  angles  to  the  axis  are  rendered 
convergent  or  divergent,  according  to  the  kind  of 
cylinder  it  is,  whether  convex  or  concave.  The 
refracting  power  of  a  cylindrical  lens  in  the  merid- 
ians, oblique  to  the  axis,  increases  regularly  from 
the  vertical  to  the  horizontal  meridian. 

A  BCD  is  a  convex  cylindrical  lens;  abed,  a  train 
of  plane  waves  entering  the  lens  parallel  to  the  axis. 
They  pass  on  through  unchanged  as  a' ,  b' ,  e' . 

Waves  I,  2,  3  are  transverse,  and  on  passing  through  the  lens  are 

rendered  convergent  to  the  point  R'. 
RR'  is  the  line  of  propagation  of  both 
the  vertical  and  horizontal  waves  of 
light.  5  and  S'  parallel  rays  of  cross- 
waves. 

ABCDEF  is  a  concave  cylinder  : 
abed,  a  train  of  plane,  vertical  waves, 
passing  through  the  lens  unaltered. 

The  cross  waves  i,  2,  3  are  rendered 
divergent  on  passing  through  the 
lens,  as  their  rays  will  show,  in  the 
figure.  RR'  is  a  ray  common  to  both 
the  vertical  and  horizontal  waves. 

The  focus  of  a  cylindrical  lens  is  a 
straight  line,  that  is,  every  point  of 
light  is  focused  as  a  line.  There  can  therefore  be  no  image  forma- 
tion by  cylindrical  lenses.    The  focal  Hne  of  a  cylinder  is  always 


42 


THE   EYE,    ITS   REFRACTIOxN   AND    DISEASES. 


parallel  to  the  axis  of  the  cylinder. 
Cylinders  are  numbered  like  spherical 
lenses  according  to  the  degree  of 
curvature  of  their  curved  surfaces  or 
according  to  their  focal  length.  The 
position  of  a  cylinder  is  described  ac- 
cording to  the  angle  at  which  its  axis 
stands  in  regard  to  the  horizontal. 
Thus:  If  the  axis  is  vertical,  we  say 
the  cylinder  is  at  90  degrees,  and 
when  the  axis  is  horizontal ;  at  o  or 
180  degrees,  and  so  on. 

A  BCD  is  a  convex  cyHnder,  O  a 
point  from  which  light  proceeds.  Lines 
a  and  d  are  rays  of  waves  that  pro- 
ceed from  the  point  O  and  enter  the 
lens  parallel  to  its  axis,  and  are  not 

refracted  but  continue  to  diverge  as  a\  b\  and  illuminate  screen  5* 

along  the  line  a"b" .     The  dotted  lines  to  the  cross  meridian  of  the 

lens  represent  waves  that  enter  the  lens  at  right  angles  to  the  axis. 

They  are  converged  and  come  together  at  the  point  O  on  the  line 

a"b".     All  light  that  enters   the  cylinder 

between  these  positions  is  focused  as  short 

lines  running  in  the  direction  of  the  merid- 
ian that  the   light   entered.     These  short 

oblique  lines  overlap  and  aid  in  building 

up  the  long  line  a"b". 

This  figure  represents  the  shape  of  the 

illumination   on  the  screen,  light  entering 

the  cylinder,  in   meridians   oblique   to  its 

axis.     The  heavy  lines  or  rays  in  each  case 

are  those  nearest  the  observer,  as  he  looks 

at  the  figure.    0'  is  the  focus  of  O,  through 

the  oblique  meridians,  but  as  these  merid- 


PRISMS  AND    LENSES. 


43 


ians  are  feebler  than  the  horizontal  meridian,  their  focus  lies  behind 
the  focus  of  the  latter,  so  that  while  the  focus  of  the  point  O  will  be 
on  the  screen  in  the  position  repre- 
sented, the  screen  will  be  illumin- 
ated in  the  direction  of  the  oblique 
lines  a'  and  b\  through  the  oblique 
meridians  a  and  b. 

If  two  or  more  spherical  lenses 
aFe  placed  together  the  strength  of 
the  combination  will  be  equal  to 
the  sum  of  the  combined  spheres. 
Thus  a  +  2,  +  3,  and+4  D.  S.  placed  together,  equals  a  lens  of  +  9  D.S. 

A  convex  and  a  concave  lens  of  the  same  strength  neutralize  each 
other,  and  such  a  combination  acts  upon  light  that  passes  through  it 
as  a  plane  glass.  We  use  the  sign  O  to  express  the  fact  that  one 
lens  is  to  be  combined  with  another.  Thus  :  —  i  D.  S.  O  (combined 
with)  +  2  D.  S.  =  +  I  D.  S. 

When  a  spherical  and  a  cylindrical  lens  are  combined,  we  call  it  a 
sphero-cylindrical  combination.  The  strength  of  such  a  combination 
is  equal  to  the  strengths  of  the  combined  lenses  in  the  direction  at 
right  angles  to  the  axis  of  the  cylinder,  while  the  cylinder  does  not 
alter  the  strength  of  the  sphere  in  the  direction  parallel  to  its  axis. 
Sphero-cylindrical  combinations  in  spectacle  lenses  are  arranged  as 
follows  :  If  the  combination  is  a  positive  one ;  and  the  cylinder  is 
weaker  than  the  sphere,  it  is  ground  on  the  side  of  the  glass  that  is 
to  be  placed  next  to  the  eye,  while  the  sphere  is  ground  on  the  other 
side.  If  the  cylinder  is  stronger  than  the  sphere,  the  spherical  side 
of  the  lens  is  placed  next  to  the  eye.  If  the  combination  is  negative, 
the  opposite  method  is  pursued,  thus  :  the  spherical  side  is  placed 
next  to  the  eye  whenever  it  is  stronger  than  the  combined  cylinder, 
and  vice  versa.  In  the  figures  below,  the  number  at  the  end  of  the 
dotted  lines  represents  the  strength  of  the  sphero-cylinder  combina- 
tion in  the  direction  of  the  axis  of  the  cylinder,  and  the  number  at  the 


44 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


end  of  the  continuous  line,  the  strength  of  the  combined  lenses  at 
right  angles  to  the  axis  of  the  cylinder.  ^5^ 

+  5  D.  S.  O  +  I  D.  Cyl.  Ax.  90°  = 
2  D.  S.  o  -  I  D.  Cyl.  Ax.  180°  =  I— -^— I-2D 


+  4  D.  S.  O  +  3  D.  C.  Ax.  45°  = 


+40 


V7D 


Never  combine  a  convex  sphere  with  a  concave  cylinder,  or  vice 
versa,  if  it  is  possible  to  avoid  doing  so,  as  such  lenses  are  more  diffi- 
cult to  grind  accurately ;  the  lens  cannot  be  made  as  thin,  and  the 
combination  possesses  more  aberration  than  when  a  sphere  and  cyl- 
inder of  like  signs  are  combined.  Thus  instead  of  ordering  +  3  D.  S. 
O  —  I  D.  Cyl.  Ax,  90°  its  equivalent  in  terms  of  plus  signs  should 
be  substituted. 

+  3  D.  S.  o  -  I  D.  C.  Ax.  90°  =  +  2  D.  S.  o  +  I  E^.  C.  Ax.  180° 

+  1  D.  S.  o-  I  D.  C.  Ax.  45°  =  + I  D.  C  Ax.  135°. 

Toric  Lenses. — A  toric  lens  is  one  which  has  a  cylindrical  and 
spherical  surface  on  the  same  side.  It  is  a  section  of  a  tore.  A 
tore  is  a  large  ring  used  at  the  base  of  a  column.  A  hard  rubber 
ring,  such  as  is  given  to  teething  children,  represents  a  tore.  The 
surface  into  which  a  positive  toric  lens  will  fit  is  a  negative  toric 
lens.  Torical  lenses  are  more  periscopic,  freer  of  aberration  than  the 
usual  sphero-cylindrical  combination,  giving  a  clearer  and  a  flatter 
field  of  view.  It  is  spherical  aberration  in  a  lens  that  causes  the 
edges  of  objects  looked  at  through  them  to  appear  blurred,  elevated 
or  curved  while  the  middle  of  the  object  is  well  defined  and  vice 


PRISMS  AND    LENSES.  ■  45 

versa.  The  torlcal  lens  is  at  present  little  used  and  is  expensive. 
It  is  best  adapted  to  correcting  the  refraction  after  cataract  extrac- 
tion. If  the  spherical  surface  in  a  toric  lens  is  stronger  than  the  cyl- 
indrical, we  speak  of  it  as  a  sphero-toric  lens,  while  if  the  cylindrical 
is  the  stronger  —  a  cylindro-toric  lens. 

To  convert  a  sphero-cylindrical  lens  into  a  sphero-toric,  divide  the 
greatest  meridian  in  half  for  the  sphere.  Subtract  this  from  each  of 
the  meridians  in  turn  for  the  strength  of  the  two  toric  curvatures. 
For  example  take  :  +  8  D.  S.  O  +  2  D.  C.  Ax.  90°. 

If  we  divide  the  greatest  meridian  in  half  we  have  +  5  D.  as  the 
power  for  the  spherical  surface  of  one  side  of  the  lens.  Subtract  5 
from  8  and  +  3  will  be  strength  of  one  toric  curve  upon  the  other  side 
of  the  lens.  Subtract  5  from  10  and  +  5  D.  will  be  the  power  of  the 
other  toric  curve.  When  the  cylindrical  element  is  the  stronger  as 
in  the  following  +  2  D.  S.  O  +  4  D.  C.  Ax.  90°,  the  strongest  merid- 
ian is  halved  for  one  surface  which  in  this  case  will  be  cylindrical 
ground  upon  one  side  of  the  lens ;  the  other  half  will  be  the  strength 
of  one  toric  curve  ground  upon  the  other  side  of  the  lens,  and  the 
weaker  meridian  the  other  toric  curve.  The  sphero-toric  equivalent 
of  the  sphero-cylindrical  combination  taken  as  example  ( +  8  D.  S. 
0  +  2  D.  C.  Ax.  90°)  is  as  follows:  +5  D.  S.  O  toric  +3  ver- 
tical and  +  5  horizontal.  And  the  cylindro-toric  :  (+  2  D.  S.  O  +  4 
D.  C.  Ax.  90°)  +3  D.  C.  Ax.  90°  O  toric  +  3  horizontal  and  +  2 
vertical. 

One  of  the  most  useful  apparatuses  for  the  study  of  the  laws  of 
refraction  and  reflection  is  the  one  shown  in  the  cut.  It  consists  of 
a  graduated  brass  circle  mounted  in  a  vertical  plane  upon  a  tripod. 
Two  slides  move  around  the  circumference  ;  on  one  of  them  there  is 
a  piece  of  ground  glass,  P,  and  on  the  other  is  an  opaque  screen,  S, 
in  the  center  of  which  there  is  a  small  aperture  ;  fixed  on  the  latter 
sHde  there  is  also  a  mirror,  M,  which  can  be  more  or  less  rotated  but 
remains  always  in  the  plane  at  right  angles  to  that  of  the  graduated 
circle.  Lastly,  there  is  at  the  center  of  the  circle  a  small  stage  O, 
upon  which  a  mirror  may  be  placed  for  studying  reflection  or  replaced 


46 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


by  a  hollow  semicircular  vessel,  for  the  reception  of  liquids  for  the 
study  of  refraction.  The  following  method  of  using  the  instrument 
is  taken  from  Ganot's  "Physics."  To  study  refraction:  The  stage 
in  the  center  of  the  graduated  arc  is  replaced  by  a  semicircular 
vessel  filled  with  water  until  its  surface  is  at  the  height  of  the  center 
of  the  circle.  The  mirror  M  is  then  so  inclined  that  light  passes 
through  the  central  opening  in  the  screen  S,  and  falls  upon  the  sur- 
face of  the  water  at  the  center  of  the  circle.  The  light  suffers  refrac- 
tion on  entering  the  water,  but  passes 
straight  out  of  the  vessel  below,  as 
it  is  perpendicular  to  the  curved  side 
of  the  vessel.  The  arm  carrying  P 
(a  piece  of  ground  glass)  is  then 
moved  down  until  the  refracted  ray 
is  received  upon  it  at  its  central 
point.  The  sines  of  the  angle  of  in- 
cidence and  of  the  anofle  of  refraction 
are  read  off  from  the  arms  /  and  R, 
respectively,  which  move  around  the 
circle  always  at  right  angles  to  the 
vertical  line  that  passes  through  the 
center  of  the  circle.  To  study  reflec- 
tion, a  mirror  is  placed  at  the  center 
of  the  graduated  circle,  with  its  sur- 
face horizontal.  Light  is  conveyed 
to  it  through  the  central  opening  in 
the  opaque  screen,  S,  and  the  amount 
of  the  angle  of  incidence  and  of  the  angle  of  reflection  read  off  from 
the  circumference  of  the  circle  after  the  arm  carrying  the  screen  P 
has  been  placed  in  position  to  receive  the  reflected  ray  of  light,  upon 
the  center  of  the  screen  P.  In  the  above  cut,  xcc'  =  angle  of  inci- 
dence ;  (fey  =  angle  of  reflection  ;  x'cy'  =  angle  of  refraction. 


CHAPTER   III 

MIRRORS    AND    THE    REFLECTION    OF    LIGHT 

A  MIRROR  is  any  polished,  smooth  surface  that  separates  two  media 
of^  different  densities,  and  which  shows  by  reflection  the  image  of  an 
object  presented  to  it.  By  the  reflection  of  Hght  is  meant  the  send- 
ing back  or  returning  of  light  when  it  meets  a  polished  smooth  sur- 
face. At  the  surfaces  of  all  refracting  media,  light  undergoes  both 
refraction  and  reflection,  each  interfering  with  the  distinctness  of 
image  formation  by  the  other.  It  is  impossible  to  make  a  refracting 
medium  that  will  not  have  some  power  in  reflecting  light.  For,  if 
the  surface  of  the  medium  be  made  rough  or  its  polish  be  otherwise 
interfered  with,^  the  substance  becomes  nearly  opaque  from  the  ir- 
regular refraction  and  reflection  on  its  surface.  The  substance  of 
which  a  mirror  is  made  must  be  opaque  if  we  wish  to  obtain  the  best 
image  by  reflection.  If  the  mirror  is  transparent,  part  of  the  lumin- 
osity of  the  image  is  lost  by  a  portion  of  the  light  from  the  object 
passing  through  the  mirror.  As  a  rule  mirrors  are  made  of  glass 
backed  with  amalgam,  or  of  a  highly  polished  metal.  Mirrors  are 
divided  according  to  the  shape  of  their  reflecting  surfaces  into  plane, 
concave  and  convex.  The  light  that  comes  to  a  mirror  is  the  inci- 
dent light,  and,  after  it  is  returned  by  the  mirror,  the  reflected  light. 
The  angle  of  incidence  is  that  formed  between  the  normal  or  radius 
to  the  wave-front  and  that  of  the  mirror,  at  the  point  of  incidence  ; 
the  angle  of  reflection,  as  the  angle  between  the  normal  of  the 
reflected  ray  and  that  of  the  mirror.  The  two  following  laws  are 
observed  in  the  reflection  of  light : 

(i)  The  angle  of  reflection  is  always  equal  to  the  angle  of  incidence, 
and  (2)  the  incident  and  the  reflected  rays  occupy  the  same  plane. 
In  the  figure  below  M  is  the  face  of  a  plane  mirror ;  a,  b,  c,  d  are 

47 


48 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


plane  waves,  incident  to  the  mirror  ;  a\  b',  c'  and  d\  the  same  waves 
after  reflection. 

Angle  INO,  angle  of  incidence  ;  ONR,  angle  of  reflection.  If  the 
waves  are  parallel  to  the  face  of  a  plane  mirror  on  incidence,  the 

light  is  returned  back  along  the  same  course. 
Under  these  conditions  the  value  of  the  an- 
gle of  incidence  is  zero,  and  the  angle  of 
reflection  is  likewise  zero.  A  plane  mirror 
does  not  alter  the  relation  of  rays  of  light 
that  fall  upon  it.  If  they  were  parallel  be- 
fore incidence,  they  are  so  after  reflection. 
If  divergent  or  convergent,  they  are  equally  so  after  reflection.  The 
action  of  the  mirror  is  to  change  the  direction  of  the  light  in  reflec- 
tion, so  that  it  appears  to  start  from  a  point  behind  the  mirror,  its 
virtual  focus. 

The  image  formed  by  a  plane  mirror  is  upright,  of  the  same  size 
as  the  object,  virtual,  on  a  line  at  right  angles  to  the  mirror  from  the 
object,  and  behind  the  mirror  at  a  distance  equal  to  the  distance  of 
the  object  in  front  of  the  mirror. 

•  M  is  a  plane  mirror  ;  (9,  an  object  presented  to  it.  Draw  rays  a 
and  b,  from  the  head  of  the  arrow  to  mirror.  Erecj;  perpendiculars 
at  the  points  of  incidence.  Make  the 
angles  of  reflection  equal  to  the  angles 
of  incidence.  Project  the  reflected  rays 
back  behind  the  mirror  and  where  they 
come  to  a  virtual  focus  is  the  point  in 
the  image  corresponding  to  the  head  of 
the  object  (arrow).  We  can  ascertain  a 
point  in  the  image  corresponding  to  any 
point  in  the  object  by  drawing  a  line  per- 
pendicular to  the  mirror  (extending  its  length,  if  necessary,  in  order 
to  get  the  perpendicular  line  to  strike  it)  from  the  given  point  in  the 
object,  and  measuring  off  on  this  line  posterior  to  the  mirror  a  dis- 
tance equal  to  the  distance  of  the  point  in  the  object  in  front  of  the 


MIRRORS   AND    THE   REFLECTION   OF    LIGHT. 


49 


mirror.  When  a  mirror  is  rotated,  that  is  when  its  normal  (a  Hne 
perpendicular  to  its  surface)  is  made  to  incline  in  different  direc- 
tions, the  reflected  ray  passes  through  twice  the 
angle  of  rotation  of  the  mirror.  m' 

Let  X  be  an  incident  ray  to  the  mirror  M,  at  / 
the  point  O.  Being  perpendicular  to  the  mirror, 
it  is  reflected  back  along  the  same  path.  Rotate 
M  to  M' .  Normal  x  moves  to  y,  through  angle  xoy,  the  angle 
of  rotation  of  the  mirror.  Ray  x  passes  off  in  the  direction  of 
x\  making  angle  xoy  equal  to  angle  yox' .  While  normal  x  has 
moved  through  angle  xoy,  ray  x  has  moved  through  xox' ,  which  is 
twice  angle  xoy.     The  image  formed  by  a  plane  mirror  moves  in  a 

J direction  opposite  to  the  rotation  of  the  mirror. 

1 1      \  /   \o        /is  the  image  of  O,  when  mirror  is  in  posi- 

tion M.  When  the  face  of  mirror  is  inclined 
upwards,  the  image  of  O  descends  to  /',  and 
vice  versa. 

Spherical  mirrors  are  those  whose  surfaces 
are  portions  of  hollow  spheres.  If  the  concave 
side  is  turned  towards  the  object,  the  mirror' 
is  concave  and  if  the  convex  side  is  next  to  object  we  have  a  con- 
vex mirror.  In  each  case  the  center  of  the  sphere,  of  which  the 
mirror  forms  a  part,  is  the  center  of  curvature  of  the  mirror.  The 
central  point  on  the  surface  of  a  mirror  (spherical),  is  called  its  vertex. 
A  line  joining  the  center  of  curvature  and  the  vertex  is  the  principal 
axis.  Any  line  passing  through  the 
center  of  curvature,  but  not  through 
the  vertex,  is  a  secondary  axis  of  the 
mirror.  The  radius  of  curvature  is 
the  radius  of  the  sphere  of  which  the 
mirror  forms  a  part,  a  line  drawn  from 
the  center  of  curvature  to  the  mirror. 

Mirror  M  is  concave  to  object  A\   C  \s  its  center  of  curvature  ; 
Ca,  its  principal  axis  ;  and,  Cb,  a.  secondary  axis.     M'  is  convex  to  A, 

4 


50 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


and  Ca',  its  principal  axis  ;  Cb',  a  secondary  axis.  Spherical  mirrors 
may  be  supposed  to  be  made  up  of  a  number  of  plane  mirrors,  per- 
pendicular to  the  radii  of  curvature  of  the  mirror. 


a    b 


REFLECTION    FROM    AND    IMAGE    FORMATION    BY    CONCAVE    MIRRORS. 

When  parallel  light  strikes  a  concave  mirror,  it  is  reflected  from  the 
mirror  convergent,  and  is  gathered  to  a  point,  called  the  principal 
focus  of  the  mirror.  The  distance  of  this  point  from  the  mirror  marks 
the  strength  of  the  mirror.     If  light  emanates  from  the  principal  focus 

it  is  reflected  from  the  mirror  parallel. 
As  in  convex  lenses  the  more  divergent 
the  rays  of  light  that  impinge  upon  the 
mirror,  the  further  off  is  its  focus.  Di- 
vergent rays  coming  to  a  mirror  from  a 
near  point  are  focused  beyond  the  prin- 
cipal focus. 

This  secondary  focus  and  the  point 
from  which  the  light  emanates  are  to  each  other  as  conjugate  foci. 

M  is  a  concave  mirror ;  RC,  its  radius  of  curvature  ;  a,  b,  c,  etc., 
a  train  of  plane  waves,  advancing  towards  the  mirror.  They  are 
reflected  back  as  negative  waves  a',  b',  c',  converging  to  the  point  /^ 
the  principal  focus  of  the  mirror. 
jFC  is  the  focal  length  of  the  mirror. 
Convex  or  positive  waves  eman- 
ate from  the  point  C.  They  pass 
to  mirror,  upon  which  the  ends  of 
the  rays  impinge  first.  The  waves 
after  reflection  are  hence  rendered 
converging  to  the  point  C,  the  conjugate  focus  of  the  point  C.  F 
is  the  point  of  the  principal  focus.  Concave  mirrors  form  real  im- 
ages, inverted,  and  on  the  same  side  of  the  mirror  as  the  object,  so 
long  as  the  object  is  further  from  the  mirror  than  its  principal  focus. 
If  the  object  is  nearer  the  mirror  than  the  principal  focus  the  image 
is  larger  than  the  object,  upright,  virtual  and  behind  the  mirror. 


MIRRORS    AND    THE    REFLECTION   OF   LIGHT. 


51 


J/  is  a  concave  mirror  ;  O  an  object,  presented  to  it.  To  find  the 
position  of  the  image,  draw  rays  a  and  c  from  the  head  of  the  object 
to  the  mirror.  Ray  c,  passing  through  C, 
the  center  of  curvature  of  the  mirror,  strikes 
the  face  of  the  mirror  perpendicularly,  and 
hence  passes  back  along  the  course  of 
incidence.  Ray  a,  being  parallel  to  the 
principal  axis  b  of  the  mirror,  is  reflected 
to  tfie  principal  focus  F.  Where  ray  a' 
crosses  the  ray  c,  is  formed  the  head  of 
the  image  /,  the  tail  of  the  image  being  on  the  principal  axis. 


OBJECT    NEARER   THE    MIRROR   THAN    THE    PRINCIPAL    FOCUS. 

F  is  the  principal  focus ;  O  is  nearer  the  mirror  than  F.  Draw 
from  the  head  of  the  object  ray  a  parallel  to  the  principal  axis  of  the 
mirror  ;  it  will  be  reflected  through  the  point  F.  Draw  ray  b  diverging 
to  mirror  ;  it  will  be  reflected  and  focused  at  a  point  further  from  the 
mirror  than  the  principal  focus.  Where  reflected  rays  a'  and  b'  cross 
will  be  found  the  head  of  the  image  /.  As  the  foot  of  the  object 
rests  upon  the  principal  axis,  the  foot  of  the  image  will  do  likewise. 
If  the  object  is  beyond  the  center  of  curvature  of  the  mirror,  the 
image  is  smaller  than  the  object  and  is  situated  between  the  principal 
focus  and  center  of  curvature  of  the  mirror.  The  converse  is  also 
true,  that  if  the  object  is  situated  between  the  principal  focus  and  the 

center  of  curvature,  the  im- 
age will  be  larger  than  the 
object  and  situated  beyond 
the  center  of  curvature.  The 
image  will  be  inverted  in 
each  case.  (See  figure 
above.)  The  light  that  em- 
anates from  the  center  of 
curvature  of  a  concave  mirror  strikes  one  of  the  plane  mirrors  of 
which  the  spherical  mirror  is  made  up,  and  is  reflected  back  along 


-^'-^ 


52 


THE   EYE,-  ITS    REFRACTION   AND    DISEASES. 


the  same  path.  There  is  consequently  no  image  formed  as  image 
and  object  overlap  each  other.  As  in  lenses,  so  in  mirrors,  the 
shorter  the  focus  the  stronger  the  mirror.     The  shorter  the  radius 

of  curvature,  the  smaller  the  imagfe 
formed  by  the  mirror.  The  focal  inter- 
val of  a  concave  mirror  is  equal  to  one 
half  the  radius  of  curvature,  expressed  : 

F=Rl2. 

In  the  figure,  p,  is  one  of  the  plane 
mirrors  of  which  the  concave  mirror  M 
is  composed  ;  Cd,  the  radius  of  curvature  of  the  mirror  is  normal 
to  it ;  ray  a  is  parallel  to  PP',  the  principal  axis  of  the  mirror. 
Angle  i  and  angle  r  are  equal,  since  the  angle  of  incidence  and 
the  angle  of  reflection  are  equal.  Angle  i  =  angle  x,  being  alternate  ; 
Therefore  CP=  Fd,  being  sides  of  a  triangle  opposite  equal  angles. 
Fd  =  FP,  and  therefore 


CF==  FP'     or     FP'  =  CP'l2  =  Rji, 


as 


CP'  =  R. 


The  conjugate  focus  of  any  point  at  a  greater  distance  than  the 
principal  focus  is  found  according  to  the  following  formula : 

i//+i//'  =  i/i^    or      i//'  =  i//r_i/y; 

in  which  F=  distance  of  the  principal  focus  from  the  mirror  ;  /',  dis- 
tance of  conjugate  focus  or  image 
from  the  mirror  ;  and  f,  the  dis- 
tance of  the  source  of  light  or 
object  from  the  mirror. 

The  linear  dimensions  of  an 
object  and  its  image  are  to  each 
other  as  their  distances  from  the 
mirror. 

Let  BA  be  the  object,  and  denote  it  by  (9 ;  A'B',  its  image,  and 
denote  it  by  i.     Let  AF=  D  and  A'F=  d  and  FV=  F. 


MIRRORS   AND   THE    REFLECTION   OF   LIGHT. 


53 


The  triangles  BAFand  B'FV,  on  one  side  and  FVX  and  A'B'F 
on  the  other,  give  the  relations  0/z  =  DfF=  F/d,  or  Dd=  FF. 
Oji  =  Dj F C2in  also  be  written  Oli=  2DI R* 

Let  ^F=/and  A'V=f'.  As  D=f-F  and  d=f'-F,  the 
formula,  that  of  Newton,  Dd=  FF,  can  be  written  thus : 


or 


Flf+Flf'  =  i     or     ilf+if'  =  ilF 
I  I 


Distance  of  object  from  mirror     Distance  of  image     Focal  interval 

0:i\:  AF:  A'F  and  O -.i  :  :  AV:  A' V.     LetAV=  D,  and 

A'  V=  d,  then  Oji  =  Djd. 

A  mirror  has  a  20-cm.  focus  ;   light  comes  to  it  from  a  distance  of 
30  cm.     How  far  off  is  the  conjugate  focus  ? 

I  If  =  i/F—  i//=  1/20—  1/30=  1/60,    /'  =  60  cm. 

Convex  Mirrors.  —  All  rays  of  light  impinging  upon  a  convex 
mirror  are  rendered  divergent.  If  they  were  divergent  on  incidence, 
they  are  more  so  after  reflection.  The  foci  and  images  of  convex 
spherical  mirrors  are  virtual,  and 
back  of  the  mirror.  The  images 
are  smaller  than  the  objects. 

Let  C  be  the  center  of  curva- 
ture of  the  convex  mirror  M] 
AB,  an  object ;  CC\  the  princi- 
pal axis  of  the  mirror.  To  locate 
image  draw  ray  i  parallel  to  the 
axis  CO ;  it  will  be  reflected  off  in 
the  direction  of  x,  having  a  virtual  focus  at  ^behind  the  mirror.  Draw 
i'  so  that  it  will  pass  through  the  center  of  curvature  of  the  mirror. 
It  will  then  strike  the  mirror  at  right  angles  and  be  reflected  back 
along  the  same  path.     The  reflected  rays  appear  to  originate  from 

»  This  formula  is  the  one  used  in  ophthalmometry. 


54  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

the  point  A'  behind  the  mirror,  the  point  corresponding  to  the  point 
A  of  image.  As  in  concave  mirrors  the  focal  interval  is  equal  to 
one  half  of  the  radius  of  curvature.  Conjugate  focal  distances  are 
ascertained  for  convex  mirrors  by  the  same  formula  as  for  concave 
mirrors,  save  a  minus  sign  is  placed  before  F  and  /',  as  both  are 
virtual  and  have  a  negative  value,  being  behind  the  mirror.  The 
formula  becomes  then:  \\ f—  \\ f'  =  —  \\ F.  Find  the  conjugate 
focus  of  a  point  at  60  cm.  in  front  of  a  convex  mirror  of  20  cm.  radius 
of  curvature.     F=io,f=6o. 

^If-  i//'  =  -  i/^     i//=-  I / 10 +1/60  =  -5/60;/=-  12  cm. 

The  conjugate  focus  is  12  cm.,  behind  the  mirror. 

From  the  following  proportion  it  is  easy  to  calculate  the  radius  of 
curvature  of  a  convex  mirror,  or  any  other  of  the  unknown  quantities 
in  the  proportion,  if  the  remaining  three  quantities  are  given. 

^  radius  of  curvature  _  Distance  of  object  from  the  mirror 
Length  of  image  Length  of  object 

See  page  53,  formula  011=  DJF. 

If  one  half  the  radius  of  curvature  =  F  (focal  length  of  mirror) ; 

length  of  image,   /;  distance  of  object  from  mirror,  D ;  length  of 

object  O ;  we  have  ^   ^ 

F=  • 

O 

Example :  What  is  the  focal  length  of  a  mirror,  if  an  object  i  cm. 
in  size,  at  a  distance  of  10  cm.,  is  reduced  in  the  image  to  i  mm.? 

„     ID     100  mm. 

r  =  --pz-  = =  10  mm. 

O         10  mm. 

Ascertain  the  size  of  an  image  of  an  object  i  cm.  in  size,  at  a  dis- 
tance of  10  cm.  formed  by  a  mirror  of  10  mm.  focus. 

r.     I  •  D                        I '  100  mm.       _ 
r  =     ^    ,      10  mm.  = =  /  •  10  mm. 

O  ^       10  mm. 

ergo  :  /  =  I  mm. 


MIRRORS   AND   THE   REFLECTION   OF   LIGHT. 


55 


What  has  been  said  in  the  preceding  pages  about  spherical  mir- 
rors, applies  only  to  mirrors  of  small  apertures  (see  aperture  of 
lenses),  or  to  small  portions  immediately  around  the  axis  of  the  mir- 
ror if  large.  The  phenomena  of  reflec- 
tion are  not  so  simple  about  the  edge  of 
a  large  mirror.  Mirrors  as  lenses  pos- 
sess aberration.  The  peripheral  rays  of 
light  are  brought  to  a  focus  anterior  to 
that  of  the  central  rays.  Every  re- 
flected ray  cuts  the  one  next  to  it,  and  their  points  of  intersection 
form  in  space  a  curved  surface  which  is  called  a  caustic  by  reflection. 

The  figure  represents  a  number  of  parallel  rays  impinging  upon 
the  mirror.  Those  on  the  edge  are  focused  nearest  the  mirror,  and 
those  nearest  the  center  furthest  from  the  mirror.  The  intersection 
of  the  reflected  rays  forms  a  curved  area  of  illumination,  which  in 
section  has  the  shape  of  the  dotted  lines. 


.y\ 

Caustic 

:/\ 

Cur^e  . 

\ 

..^J^ 

"^  "^^^^^ 

-^____ 

V-"""^/ 

■•\\/ 

■•A/ 

CHAPTER  IV 

THE  EYE,  AND  THE  THEORY  OF  GAUSS 

The  human  eyeball  is  more  nearly  a  sphere  than  the  eyeball  of 
any  other  animal.  It  is  enclosed  within  a  bony  socket ;  protected  an- 
teriorly by  the  lids  ;  rests  upon  a  fatty  cushion  ;  held  in  place  by 
fascia  ;  moved  by  six  muscles  ;  supplied  by  many  vessels  and  nerves 
and  provided  with  an  apparatus  to  keep  it  moist — the  lachrymal  ap- 
paratus. The  eyeball  by  outside  measurements  is  on  the  average, 
antero-posteriorly,  24  mm.;  transversely,  23.5  mm.,  and  vertically 
23  mm. 

The  eyeball  consists  of  three  coats  or  tunics  : 

1°.  The  external  fibrous  tunic,  formed  by  the  cornea  and  the 
sclera. 

2°.  The  middle  or  vascular  tunic,  called  the  uvea,  formed  by  the 
iris,  ciliary  processes,  and  the  chorioid. 

3°.  The  inner  or  nervous  tunic,  formed  by  the  retina. 

The  posterior  four  fifths  of  the  outer  coat  of  the  eye  globe  is 
formed  by  the  opaque  sclera,  in  shape  conforming  nearly  to  that  of 
a  sphere  ;  the  anterior  one  fifth,  by  the  transparent  cornea,  which  re- 
sembles in  its  curve  that  of  an  ellipse.  The  cornea  is  not  set  upon 
the  anterior  portion  of  the  sclera,  after  the  manner  of  a  watch-crystal 
upon  the  face  of  a  watch,  as  is  so  often  stated,  but  the  junction  of 
these  segments  is  marked  by  a  broad,  shallow,  annular  groove,  the 
sulcus  sclerae.  It  is  on  account  of  this  groove  that  the  cornea  seems 
to  set  upon  the  sclera.  If  it  were  not  for  this  sulcus  the  curve  of 
the  sclera  and  that  of  the  cornea  would  be  a  nearly  continuous  one. 
The  middle  coat  is  the  nourishing  tunic  of  the  eyeball.  It  is  formed 
by  the  iris  in  front  with  its  central  hole  or  pupil,  by  the  chorioid  be- 
hind, and  by  the  ciliary  processes  between  the  two.     The  iris  arises 

56 


THE    EYE,    AND   THE    THEORY    OF    GAUSS.  57 

just  posterior  to  the  junction  of  the  cornea  with  the  sclera.  It  rests 
by  its  pupillary  border  upon  the  crystalline  lens  which  is  immediately 
behind  it.  The  crystalline  lens  is  a  bi-convex  lens.  It  is  surrounded 
by  its  capsule,  and  swung  in  its  suspensory  ligament  arising  from  the 
ciliary  processes.  The  i^tnet-coat  lines  the  interior  of  the  eyeball, 
posterior  to  the  ciliary  processes.  The  cavity  enclosed  by  these 
tunics  is  divided  by  the  lens  and  its  suspensory  ligament  into  two. 
The*  posterior  cavity  is  filled  by  the  vitreous  humor  (the  vitreous 
chamber),  and  the  anterior  cavity,  by  the  aqueous  humor.  The 
latter  is  divided  into  two  by  the  iris,  namely :  an  anterior  chamber, 
in  front  of  the  iris,  and  a  posterior  chamber,  behind  the  iris  and  in 
front  of  the  lens.  Both  of  these  chambers  are  filled  with  a  watery 
lymph  secreted  by  the  ciliary  processes  and  iris,  the  aqueous.  The 
anterior  and  the  posterior  chambers  communicate  by  means  of  the 
pupil.  The  dioptric  media  of  the  eye  are  the  cornea,  aqueous 
humor,  crystalline  lens  and  the  vitreous  humor,  which  acting  upon 
light  that  enters  the  eyeball,  bring  it  to  a  focus  upon  the  retina.  The 
stimulus  is  then  carried  to  the  brain,  where  the  picture  formed  upon 
the  retina  is  interpreted.  The  dioptric  surfaces  of  the  eyeball  are 
four  in  number,  namely  :  The  anterior  and  posterior  corneal  surfaces 
and  the  anterior  and  posterior  surfaces  of  the  crystalline  lens.  The 
posterior  corneal  surface  is  usually  omitted  because  the  index  of  re- 
fraction of  the  cornea  and  of  the  aqueous  are  so  nearly  equal.  This 
surface,  however,  exercises  a  definite  influence  over  the  refraction  of 
light  entering  the  eye,  as  its  catoptric  image  is  well  marked.  If  the 
indices  of  refraction  of  the  cornea  and  aqueous  were  identical  there 
would  be  no  image  of  reflection  formed  by  the  posterior  surface  of 
the  cornea.  The  indices  of  the  cornea  and  aqueous  differ  more  than 
was  formerly  supposed.  The  eye  in  the  arrangements  of  its  parts  and 
in  the  manner  of  its  working  resembles  the  photographer's  camera  or 
camera  obscura,  in  which  the  eyelids  represent  the  stop-shutter ;  the 
iris  the  diaphragm  ;  the  dioptric  system  of  the  eye  the  focusing  ap- 
paratus, and  the  retina,  the  sensitized  plate  or  film.  In  the  camera 
the  sensitive  film  or  the  lens  is  movable,  in  order  that  all  objects,  at 


58  THE   EYE,    ITS   REFRACTION   AND    DISEASES.        / 

whatever  distance,  may  be  brought  to  an  accurate  focus  on  the  film, 
inasmuch  as  the  nearer  the  object  to  the  lens  the  further  behind  the 
lens  is  its  image.  In  the  human  eye  however  the  focusing  is  done 
by  a  change  in  shape,  and  consequently,  a  change  in  the  strength  of 
the  crystalline  lens.  This  act  is  called  accommodation.  It  is  only 
needed  when  the  eye  adjusts  itself  for  a  distance  nearer  than  twenty 
feet,  or  six  meters,  as  from  beyond  this  distance  the  waves  of  light  that 
reach  the  eye  are  so  nearly  plane  that  in  practice  they  may  be  con- 
sidered entirely  so.  Dr.  Beer,  in  making  a  study  of  accommodation 
in  the  lower  animals,  finds  that  aquatic  animals  with  highly  developed 
eyes,  as  cephalopods  and  long  fishes,  have  eyes  that  are  normally 
adapted  for  near  seeing.  Such  eyes  undergo  active  accommodation 
for  distant  seeing.  The  round  lens  is  brought  nearer  to  the  retina 
without  changing  its  shape.  The  eyes  of  the  terrestrial  vertebrates 
are  normally  adjusted  for  distant  seeing  and  undergo  active  accom- 
modation for  near  objects. 

In  amphibia  and  snakes  the  unaltered  lens  is  carried  away  from 
the  retina ;  in  the  rest  there  is  a  change  in  its  curvature.  In  every 
class  of  animals  except  cuttle-fishes  and  birds  there  is  a  certain 
species  whose  eyes  do  not  possess  the  power  of  accommodation. 

Some  of  these  nocturnal  in  their  habits  have  pupils  that  contract  to 
a  linear  form  when  exposed  to  light,  forming  a  sort  of  accommoda- 
tion. Cave-dwelling  and  subterranean  animals  have  but  poor  vision 
and  need  no  accommodation.  No  animal  can  see  equally  well  in 
water  and  on  the  land  without  the  use  of  accommodation.  Aquatic 
animals  are  extremely  myopic  when  on  land,  and  terrestrial  animals 
very  hyperopic  when  in  water.  Animals  that  alter  the  accommoda- 
tion by  altering  the  distance  of  the  lens  from  the  retina,  do  not  be- 
come presbyopic  as  do  those  that  accommodate  by  changing  the 
shape  of  the  crystalline  lens.     (See  Presbyopia.) 

The  normally  refracting  eye  is  called  emmetropic  {iixixeTpo<s,  in  due 
measure,  and  on/f,  eye),  and  is  denoted  by  the  letter  £.  The  retina 
of  such  an  eye  lies  at  the  principal  focus  of  its  dioptric  system.  This 
eye  without  accommodation  (at  rest)  is  adjusted  for  distant  or  plane 


THE    EYE,    AND    THE    THEORY   OF   GAUSS.  59 

waves  (parallel  rays)  of  light.  By  the  refraction  of  an  eye  we  mean 
the  state  of  its  refraction  when  at  rest,  the  relation  of  its  retina  to  the 
principal  focus  of  its  dioptric  system.  If  the  eyeball  is  too  short  from 
before  backward,  so  that  the  retina  lies  anterior  to  the  principal  focus 
of  its  dioptric  system,  the  eye  is  far-sighted  or  hypermetropic,  abbre- 
viated to  hyperopia,  and  denoted  by  the  letter  H  {vTrep,  in  excess  of, 
and  anj},  sight).  Such  an  eye  is  too  little  refractive.  The  opposite 
condition,  where  the  eyeball  is  too  long,  so  that  the  retina  lies  pos- 
terior to  the  principal  focus  of  the  dioptric  media  of  the  eye,  consti- 
tutes myopia,  denoted  by  M.  The  myopic  eye  is  the  near-sighted 
eye.  It  is  so  called  from  the  habit  that  myopes  have  of  squinting 
{fiveuv,  to  close  the  eyes,  and  anjj,  eye). 

The  myopic  eye  is  over-refractive,  in  regard  to  the  position  of  its 
retina. 

In  order  that  the  rays  of  light,  as  they  pass  through  the  dioptric 
media  of  the  eye,  may  be  traced  to  the  formation  of  images  on  the 
retina,  one  must  know  the  curyature  of  the  dioptric  surfaces,  their 
distances  apart  and  their  indices  of  refraction.  As  the  two  surfaces 
of  the  cornea  in  the  pupillary  area  are  practically  parallel  and  as  the 
indices  of  refraction  of  the  cornea  and  of  the  aqueous  humor  are 
nearly  equal,  they  are  usually  regarded  as  one  refracting  medium. 

The  refracting  or  dioptric  surfaces  of  the  eyeball  then  are  three  in 
number,  namely :  the  anterior  surface  of  the  cornea,  the  anterior 
and  the  posterior  surfaces  of  the  crystalline  lens.  The  radii  of  curva- 
ture of  each  of  the  above  surfaces  used  for  distant  vision  are  :  for  the 
cornea,  7.829  mm.;  for  the  anterior  surface  of  the  lens,  10  mm.;  for 
the  posterior  surface  of  the  lens,  6  mm.  The  indices  of  refraction  of 
the  several  media  are  as  follows  : 

Cornea  and  aqueous  humor,  1.3365  (that  of  the  cornea  and  aque- 
ous being  assumed  to  be  the  same); 

Lens,  1.437 1  ; 

Vitreous  humor,  1.3365. 

The  distance  from  the  center  of  the  cornea  to  the  center  of  the 
anterior  surface  of  the  lens  is  3.6  mm.     The  lens  is  3.6  mm.  thick 


6o  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

(on  the  average)  and  the  distance  of  the  center  of  the  posterior  sur- 
face of  the  lens  to  the  retina  1 5  mm,  Homocentric  rays  (rays  from 
a  point)  enter  the  eye  from  the  air  with  an  index  of  refraction  of 
1.00025,  into  the  cornea  with  an  index  of  1.3365.  In  passing  from 
the  rarer  to  the  denser  medium,  the  Hght  is  converged  somewhat,  to 
the  extent  that  it  would  be  brought  to  a  focus  about  10  mm.  behind 
the  retina. 

On  entering  the  lens  the  light  is  further  converged,  so  that  it  would 
come  to  a  focus  about  6.5  mm.  behind  the  retina.  The  vitreous  still 
further  converges  the  rays  to  a  focus  upon  the  retina. 

If  the  refracting  media  are  not  so  thin  that  their  thickness  can  be 
neglected  nor  so  close  together  that  their  distances  apart  can  be 
neglected,  we  find  the  position  of  the  image  by  construction  or  by  the 
rules  given  for  locating  the  image  by  a  spherical  surface  :  we  calculate 
in  the  first  place,  the  image  formed  by  the  first  dioptric  surface  ;  this 
image  then  serves  as  the  object  for  the  second  surface  and  so  on. 
We  can  thus  follow  the  rays  of  light  as  they  pass  through  the  refract- 
ing media  of  the  eyeball,  but  the  conditions  vary  for  every  distance 
of  the  object  from  the  eye,  from  which  the  light  proceeds.  To  facili- 
tate such  calculations,  schematic  eyes  have  been  devised.  Gauss 
showed  that  every  complicated  dioptric  system  can.  be  reduced  to, 
or  replaced  by,  a  single  dioptric  medium,  composed  of  six  cardinal 


V-ertex  Cexiler  or  Curvature 


points  and  six  cardinal  planes  perpendicular  to  a  common  axis,  e.  g., 
two  focal  points  ;  two  principal  points,  and  two  nodal  points.  The 
cardinal  planes  are  planes  through  the  cardinal  points  at  right  angles 
to  the  common  axis  (focal,  principal  and  nodal  planes).  There  may 
be  named  four  cardinal  points  for  every  dioptric  surface.     They  are 


THE   EYE,    AND   THE   THEORY   OF  GAUSS. 


6i 


•'??,"  the  center  of  curvature  of  the  surface;  "z/,"  the  vertex  of  the 
surface ;  F'  and  F^,  the  first  and  second  principal  foci. 

Properties  of  Cardinal  Points. — The  first  focal  point  has  the  prop- 
erty that  every  ray  of  light  that  passes  through  it  before  refraction 
is  parallel  to  the  principal  axis  after  refraction. 

Rays  that  are  parallel  on  incidence  are  focused  at  the  second  or 
posterior  principal  focus  F"^.  The  second  principal  point  is  the 
image  of  the  first  principal  point :  that  is,  rays  that  pass  through 
the  first  principal  point  pass  through  the  second  principal  point  after 
refraction.  Planes  through  these  points  at  right  angles  to  the  axis 
are  the  principal  planes.  The  first  principal  plane  is  the  conjugate 
of  the  second,  or  the  second  principal  plane  is  the  image  of  the  first. 


a;=Ant.  Focal  DistarM 
y-Post       ., 
a—X  and  y-*8 


The  second  nodal  point  is  the  image  of  the  first  nodal  point.  Every 
ray  that  passes  through  the  first  nodal  point  prior  to  refraction  passes 
through  the  second  nodal  point  after  refraction,  and  the  rays  before 
and  after  refraction  are  parallel  to  each  other.  The  distance  of  the 
first  focal  point  to  the  first  principal  plane  is  the  anterior  focal  dis- 
tance, and  the  distance  of  the  second  focal  point  from  the  second 
principal  plane  is  the  posterior  focal  distance.  The  distance  of  the 
first  nodal  point  from  the  first  focal  point  is  equal  to  the  distance 
between  the  second  principal  plane  and  the  second  focal  point,  or  the 
second  focal  distance.     The  distance  of  the  second  nodal  point  from 


62 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


the  second  or  posterior  focal  point  is  equal  to  that  between  the  ante- 
rior principal  plane  and  the  anterior  focal  point  or  the  anterior  focal 
distance.  The  distances  of  corresponding  principal  and  nodal  points 
from  each  other  are  equal  then  to  the  differences  between  the  two 
focal  distances.  Also  the  distance  between  the  two  nodal  points  is 
equal  to  the  distance  between  the  two  principal  points.  Lastly  the 
focal  distances  are  proportional  to  the  refractive  indices  of  the  first 
and  of  the  last  dioptric  media.  The  focal  planes  pass  through  the 
axis  at  the  focal  points.  The  theory  of  Gauss  assumes  that  there  is 
a  centered  system,  that  is  that  the  optical  centers  of  the  refracting 
media  are  on  a  common  axis.  (A  condition  slightly  departed  from  in 
the  eye.) 

From  the  properties  of  cardinal  points,  the  position  of  an  image 
in  the  last  medium  may  be  determined,  and  the  course  of  the  re- 
fracted ray  in  the  last  medium  be  known  if  its  course  in  the  first 
medium  is  given. 

TO    FIND    IMAGE    IN    LAST    MEDIUM    OF    AN    OBJECT    IN    THE    FIRST. 

Let  O  be  an  object,  then  /  is  its  image.  Draw  ray  i  parallel  to 
the  axis ;  it  will  pass  through  the  posterior  focal  point  i^. 


Draw  the  nodal  ray  2  to  the  first  nodal  point  (A^) ;  it  passes  through 
the  second  unrefracted,  simply  displaced  a  little. 

Draw  ray  3  through  the  anterior  focal  point  {I\).  It  is  therefore 
parallel  to  the  axis  after  refraction.  Where  these  three  rays  cross 
after  refraction  will  be  a  point  in -the  image  corresponding  to  the 
point  A  in  the  object. 


THE  EYE,  AND  THE  THEORY  OF  GAUSS. 


63 


TO    FIND   THE    COURSE    OF   A   REFRACTED    RAY,  IN    A    LAST    MEDIUM,  OF   A 
GIVEN    RAY   IN   THE    FIRST    MEDIUM, 

Let  /  be  the  incident  ray.  Continue  it  to  the  second  principal 
plane  parallel  to  the  axis.     From  any  point  {a)  in  the  ray,  draw  lines 

1  and  2.     Line  i  parallel  to  axis  will,  after  refraction,  pass  through 
the  second  point  /^2-    Line 

2  is  the  nodal  ray.  Where 
I  and  2  cross  is  the  image 
of  the  point  "a".  a'b  is 
the  course  of  the  ray  in  the 
last  medium. 

Let  V  represent  the  in- 
dex of  refraction  of  air  which  is  taken  as  the  standard  and  assumed 
to  be  equal  to  i ,  and  V  the  index  of  any  other  medium  ;  F'  the  an- 
terior or  first  focal  point ;  P\  the  posterior  or  second  focal  point 

and  f  and  f"  any  other  two  focal 
points  anterior  and  posterior  respec- 
tively, and  we  have  the  most  im- 
portant formula  in  all  geometrical 
optics.  By  it  we  can  obtain  the 
position  of  the  first  and  second  focal 
points,  or  these  given  ascertain  the 
radius  of  the  refracting  surface. 

V  —  V 
V'lf"-Vlf'=—^.    (I) 

In  the  formula/"'  and/""  are  con- 
jugate to  F"  and  F'. 
The  deduction  of  the  formula  is  as  follows  : 

In  the  figure  above  let  ah  represent  the  refracting  surface  ;  LP,  its 
axis  ;  n,  its  center  of  curvature  ;  *  r,  its  radius  of  curvature  ;  IR  an 
incident  ray  of  light  that  would  pass  to  the  point  P,  if  it  was  not  re- 
fracted. It  is,  however,  bent  to  the  point  /'.  Angle  /=  angle  of 
incidence  ;  angle  R,  the  angle  of  refraction. 

*  Center  of  ah  should  be  at  n  instead  of  at  P'  as  in  figure. 


64  THE   EYE,   ITS    REFRACTION   AND    DISEASES. 

In  triangles  reg  and  re'g\ 

sine  /         ,    /  X  1       sine  R  ,     ,, 

sine^  =  ^/^W     =^"^       sii^  =  ^/^(*)- 

Divide  equation  rt;  by  <5  to  eliminate  d,  and  we  have 

sine  /         ,.    , 
Sine  R     ^    '^ 

Letting  the  index  of  refraction  of  the  first  medium  be  /^and  that 
of  the  second  V'  as  mentioned  above,  and  K  however  accentuated 
be  equal  to  i  j  V,  the  equation  of  Snell,  sin  //sin  R  =  vlv',  becomes 
sin  /F=sin  RV. 

V' I  V=  ge' Ig'e  (3).  As  e  is/"',  and  e'  \^f",  the  equation  becomes 
V' I  V=  gf" Ig'f'.  Giving  g  its  value  oi  f'  —r,  and  g'  its  value  of 
f"  —  r,  in  the  figure  above  we  have  the  following : 

'  {J"-rV" 

which  may  be  reduced  to  the  following  form : 

V  —  V 
V  If"  -  VI f  =  ^-y^.       '■         Q.  E.  D. 

To  find  F\  the  anterior  principal  focal  point,  givey""  in  the  formula 
the  value  of  00,  as  the  center  of  curvature  of  waves  brought  to  a 
focus  at  F',  lies  at  an  infinite  distance,  i  //""( V'  j /")  =  o,  and  there- 
fore disappears  from  the  equation.  We  have  theny'  =  J/rf  V  —  V, 
for  F'  (4).  To  find  the  second  or  posterior  principal  focal  point,  or 
F",  proceed  in  the  same  way,  giving  f  the  value  of  infinity.  The 
equation  then  becomes/""  =  V'rj  V  —  V,  for  F"  (5). 

Light  enters  a  curved  glass  surface  having  a  radius  of  10  cm.  As- 
certain the  positions  of  points  F'  and  F".  The  index  of  refraction  of 
the  glass  equals  1.54,  and  that  of  air  i.  The  surface  ^  is  positive  to 
waves  emanating  from  the  side  of  F"  and  negatiAC  to  those  pro- 


THE    EYE,    AND  THE   THEORY   OF   GAUSS.  65 

ceeding  from  the  side  of  F" ,  convex  to  ray  a,  and  concave  to  ray 
a'.     Find  F'  and  F" . 

f"  =  V'rj  V  -  F=  1.54  X  10/ 1.54-  1  =  i5.4/.54  =  28.5. 

I(  the  surface  is  concave  to  the  incident  rays  r  =  —  10, 

/'  =  -  VrlV-  F=-28.5, 

the  —  sign  showing  that  the  incident  rays  are  negative  to  surface. 
If  the  surface  is  a  mirror  V=  —  V'  and  formula  is  written  thus : 

/=  -  V'r\  V  -  (-  V) 

/=  -  — ^  ^  2 =  1 5.40/3.08  =  5. 

■^  1. 54+1. 54  ^^  *^  ^ 

We  have  the  same  value  for  f'  and  f",  showing  that  in  spherical 
mirrors  both  concave  and  convex  the  focal  interval  is  equal  to  half 
the  radius  of  curvature.  When  the  first  and  the  second  principal 
foci  are  known,  a  simple  formula  may  be  deduced  to  ascertain  the 
position  of  the  conjugate  of  any  focal  distance.  Multiplying  equa- 
tion ( I )  by  r  we  have  : 

rV'lf"-rVlf'  =  r{V'-  V)lr. 

Dividing  each  numerator  by  K'  —  K: 

rV         _rV__ 

=  I, 


substitute  for  each  numerator  the  values  given  in  equations  (4)  and 

(5). 

F"lf"-F'lf'  =  i, 

Clearing  of  fractions  and  subtracting  F'F"  from  each  side  we  have 

F"f  +  F'f"  -/'/"  -  F'F"  =  F'F",  (F"  -/")  {/'  -F)  =  -  F"F', 

5 


66 


THE   EYE,   ITS    REFRACTION   AND   DISEASES. 


7^ 


F"        f" 


Let  c  and  c'  represent  the  distance  between  the  principal  foci  and 
the  conjugate  on  the  same  side,  and  we  will  have 

cc'  =  F'F", 

In  the  preceding  formulae  F\  F",f'  and  f"  represent  the  positions 
of  the  first  and  second,  principal  and  secondary  foci. 

c  /  c  Cardinal  points  fulfill  the  same  func- 

tion for  a  dioptric  system  that  they  do 
for  a  single  dioptric  surface.  The  focal 
points  of  a  dioptric  system  are  measured 
from  the  anterior  and  from  the  posterior  principal  points  respectively. 
MetJwds  of  Finding  the  Cardinal  Points  of  a  Given  System.  —  We 
draw  an  incident  ray  parallel  to  the  axis  and  construct  its  course  as 
shown  on  preceding  page  according  to  the  Law  of  Descartes  or  by 
the  formula  deduced  for  refraction  by  spherical  surfaces.  The  pos- 
terior focus  is  found.  The  incident  and  the  emergent  rays  are  then 
prolonged ;  their  intersection  is  situated  in  the  second  principal 
plane,  and  a  perpendicular  let  fall  from  this  point  to  the  axis,  marks 
the  second  principal  point.  Repeating  the  same  construction  with 
a  ray  coming  from  the  other  side  and  parallel  to  the  axis,  we  find 
after  the  same  manner  the  anterior  principal  focus  and  the  first  prin 
cipal  plane  and  point.  Knowing  these  four  points  we  can  deduce 
the  position  of  the 
nodal  points,  since  the 
distance  of  the  first 
nodal  point  from  the 
anterior  focus  is  equal 
to  the  distance  of  the 
second  principal  point 
to  the  posterior  focus, 
etc. 

/i  and  /a  aie  incident  rays  parallel  to  the  axis  of  the  system  S. 
F^  is  the  focus  of  /i  ;  F^  the  focus  of  /g.     Projecting  the  incident  ray 


THE   EYE,    AND   THE   THEORY   OF   GAUSS. 


67 


and  the  emergent  ray  until  they  meet  in  each  case  gives  us  the 
points  ^1  and  a<^.  These  points  lie  in  the  first  and  second  principal 
planes  respectively.  Perpendiculars  dropped  to  the  axis  of  the  sys- 
tem from  the  points  a^  and  a^  locate  the  principal  planes,  and  the 
prin'cipal  points  where  the  perpendiculars  cut  the  axis  of  the  system. 
Calculation.  —  Designate  the  two  optic  systems  that  we  wish  to 
combine  by  A  and  B  ;  their  focal  distances  by  F^,  F{  (for  system  A) 
and  by  F^'  and  F<1'  (for  system  B),  and  the  distance  of  the  posterior 
focus  of  system  A,  behind  the  anterior  focus  of  system  B,  by  d. 
The  cardinal  points  of  the  combined  system  can  then  be  ascertained 
by  means  of  the  following  formulae  : 


y 


P"  P"  P'P' 

yi J — '    ^2  — 


d 

in  which  y'  indicates  the  distance  of  the  focus  of  the  combined  sys- 
tem, behind  the  anterior  focus  of  system  A,  and  y^,  the  distance  of 
the  posterior  focus  of  the  combined  system  in  front  of  the  posterior 
focus  of  system  B.    The  deduction  of  these  formulae  is  as  follows  : 


68  THE   EYE,   ITS   REFRACTION   AND   DISEASES. 

An  incident  ray  I.R.  parallel  to  the  axis  will  pass  after  refraction 
by  the  system  A,  through  its  posterior  focus,  and  after  refraction  by 
the  system  B,  through  the  point  <^,  the  posterior  focus  of  the  com- 
bined surfaces.  The  prolongation  of  the  incident  ray  meets  the  re- 
fracted ray  at  D,  so  that  /^2  is  the  second  principal  plane  of  the  com- 
pound system.     According  to  the  formula  of  Newton  (q.  v.)  we  have 

The  figure  gives  the  following  relations : 

a_      F.I      _       F^ 


b      d+F,"     y^  +  F^' 
or 

^_F^{y,  +  F^') 

^  d+F," 


d+F," 
_F^{F,"F^'^-dFrl')   , 


d{d^-F,") 


_F^F^ 


d 

We  find  the  value  of  y'  and  of  F'  by  supposing  the  light  to  come 
from  the  other  side.  Knowing  the  focal  distance  and  the  position  of 
the  foci  it  is  easy  to  calculate  the  other  cardinal  points.  The  figure 
above  represents  a  negative  system  inasmuch  as  the  posterior  focus 
of  A  is  anterior  to  the  anterior  focus  of  B.  F^  and  /^  as  well  as  y' 
and  jj/2  are  therefore  negative.  \{  d  =  o,  parallel  rays  on  incidence 
are  parallel  after  refraction  by  the  system.  Such  a  system  is  called 
telescopic.  The  distance  d  is  called  the  interval,  it  determines  the 
character  of  the  combination. 


THE   EYE,    AND   THE   THEORY   OF   GAUSS.  69 

As  the  focal  distances  are  proportional  to  the  indices  of  the  first 
and  last  media,  they  should  be  equal  if  the  first  and  last  media  are 
identical,  which  is  true  in  all  optical  instruments.  In  such  a  case  the 
distance  of  the  anterior  focus  from  the  first  principal  point  is  equal 
to  its  distance  from  the  first  nodal  point ;  in  other  words  the  first  prin- 
cipal point  coincides  with  the  first  nodal  point,  and  the  second  prin- 
cipal point  with  the  second  nodal  point.  The  nodal  points  and  the 
optical  center  of  thick  lenses  can  be  easily  ascertained. 

Z  is  a  biconvex  spherical  lens  ;  CC\  its  primary  axis.  Draw  CA 
and  CA',  radii  of  the  respective  surfaces  of  the  lens,  parallel  to  each 
other.  A  A'  is  the  course  of  the  ray  / 
within  the  lens.  Where  A  A'  intersects 
the  axis  CC'  is  the  optical  center  of  the 
lens.  If  the  ray  /  continued  on  without 
refraction  it  would  meet  the  axis  of  the 
lens  at  the  point  JV,  the  anterior  nodal 
point,  N'  is  the  posterior  nodal  point 
and  is  located  by  projecting  the  re- 
fracted ray  backward  into  the  lens.  The 
optical  center  is  the  image  of  A^,  in  re- 
gard to  the  first  surface,  and  of  N'  in  regard  to  the  second  surface. 
In  infinitely  thin  lenses  the  nodal  points,  principal  points  and  optical 
center  all  coincide.  If  the  refracting  system  is  represented  by  a 
single  surface  both  principal  points  coincide  with  the  surface  and  the 
nodal  points  with  the  center. 

TO    FIND    THE    CARDINAL    POINTS   OF   THE    CRYSTALLINE    LENS. 

Let  us  suppose  that  the  lens  has  a  thickness  of  4  mm.,  that  the 
radius  of  curvature  of  the  anterior  surface  is  10  mm.,  and  that  of  the 
posterior  surface  6  mm.  Let  1.33  be  the  index  of  refraction  of  the 
aqueous  humor,  and  of  the  vitreous,  and  that  of  the  lens  1.06  in  rela- 
tion to  these  liquids.  (That  is  1.4371  divided  by  1.33  ;  the  index  of 
the  lens  divided  by  that  of  the  aqueous.)     In  this  case  the  system  A 


70  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

and  system  B  are  represented  by  a  single  refracting  surface.     The 
focal  distances  of  the  system  are  : 


For  A. 


F^ 

= 

Vr 

v-v 

0.06          ' 

mm. 

F,' 

= 

Vr 
V-V 

10  X  1.06  _ 
0.06 

=  177  mm. 

F," 

= 

Vr 
V-V 

-6 

=  106  mm. 

I  / 1 .06  —  I 

F^' 

= 

Vr 
V-V 

-6X  i/i. 

o6_    6     _ 

lOD 

mm. 

I  / 1.06  — 

I        0.06 

For  B. 


The  interval  d  is  the  distance  of  the  posterior  focus  of  the  system 
A,  from  the  anterior  focus  of  the  system  B ;  the  former  is  situated 
177  mm.  behind  the  anterior  surface,  the  latter  at  106  mm.  in  front 
of  the  posterior  surface  ;  the  thickness  of  the  crystalline  being  4  mm., 
we  have  d=  177  +  106  —  4  mm.  =  279  mm.,  and 

F{F4      167  X  177 

y  =  -V^  =  — '-^  =  106  mm. 

•^  a  279 

,     F^"F2"      106  X  100 

y  =  -^,—  = =  38  mm. 

-^  d  279  ^ 

_  F,'F,"  _  169X106  _  .,  ,  ^^ 

r^  =  — 7 —  = ;: —  =  63.4  mm. 

^  d  276  '^^ 

p,  _F,'F,"  _  177  X  100  _ 

r-y      J — —03.4  mm. 

^  d  279  ^  ^ 

The  anterior  focus  of  the  crystalline  lens  being  situated  106  mm. 
behind  the  anterior  focus  of  the  first  surface,  which  is  at  167  mm.,  its 
distance  as  far  as  that  surface  will  be  167  —  106  =  61  mm.,  and  as 
the  focal  distance  is  63.4  mm.,  the  first  principal  point  of  the  crystal- 
line lens  will  be  placed  2.4  mm.  behind  the  anterior  surface.     The 


THE    EYE,    AND    THE    THEORY    OF    GAUSS.  71 

second  principal  point  will  be  situated  at  an  equal  distance,  at 
100  —  38  —  63.4  =  —  1.4  mm.,  that  is  1.4  mm.  in  front  of  the  pos- 
terior surface.  Both  focal  distances  are  equal  as  they  always  are 
when  the  surrounding  media  are  alike.  The  refracting  power  of  the 
crystalline  lens  would  then  be  1/63.4  mm.  =  15.8  D. 

THE   MANNER  OF  COMBINING   THE   CORNEA  WITH  THE  CRYSTALLINE   LENS. 

Suppose  the  cornea  to  be  a  single  refracting  surface  having  a 
radius  of  6  mm.,  surrounded  in  front  by  air  {v=  i)  and  behind  by 
aqueous  {v'  =  1.33).  The  distance  of  the  anterior  surface  of  the  lens 
behind  the  anterior  surface  of  the  cornea  is  3.6  mm. 

In  this  case  the  cornea  forms  the  system  A.    Its  focal  distances  are : 

A  =  yy_ry  ""24  mm. 

r,,  V'r 

A  =  y-rz.-y  ^  32  mm. 

The  principal  points  coincide  with  the  surface.     The  focal  distances 
of  the  system  B  are  those  found  for  the  lens. 

The  interval  d  is  the  distance  from  the  posterior  focus  of  the 
cornea  to  the  anterior  focus  of  the  lens:  d=  61  mm.  +  32  —  3.6  = 
89.4.     With  these  data  we  compute  the  entire  optical   system  of 

the  eye : 

24  X  t2 
y  =  -V^-  =  8.6  mm. 
89.4 

^^^  634X^34  =  45  n.m. 

^       24  X  63.4 
F^  =  — ^ — ^-^  =  1 7  mm. 
89.4 

32  X63.4_ 
/*»  =  - — - — - —  =  22,7  mm. 
89.4 


72  THE   EYE,   ITS    REFRACTION   AND    DISEASES. 

The  anterior  and  posterior  focal  lengths  of  the  eyeball  are  then,  in 
diopters:  1/17  mm.  =  58.82  D.,  and  1.3365/22.7  mm.  =  58.8  D., 
respectively. 

The  strength  of  a  lens  is  ijF.  It  is  the  measure  of  curvature  that 
it  causes  a  wave  of  light  to  take  that  passes  through  it.     Conver- 


gence produced  by  a  single  refracting  surface  is  greater  on  the  side 
of  the  lesser  index  of  refraction. 

FJF^  =  V'l  V". 

The  strength  of  a  system  is  the  index  of  the  last  medium  divided 
by  the  principal  focal  distance  in  that  medium. 

The  Optic  System  and  Constants  of  the  Normal  Human  Eye.  —  The 
constants  must  be  known  before  we  can  deduct  the  position  of  the 
cardinal  points.  The  constants  of  the  dioptric  system  of  the  eyeball, 
or  the  relation  of  the  refracting  surfaces  to  one  another  in  regard  to 
their  distance  apart,  curvature,  etc.,  after  Tscherning  are  as  follows  : 

Position  of  the  anterior  surface  of  the  cornea o. 

Position  of  the  posterior  surface  of  the  cornea 1.15  mm. 

Position  of  the  anterior  surface  of  crystalline  lens 3.54  mm. 

Position  of  the  posterior  surface  of  the  lens 7.60  mm. 

Radius  of  the  anterior  surface  of  the  cornea 7.98  mm. 

Radius  of  the  posterior  surface  of  the  cornea 6.22  mm. 

Radius  of  the  anterior  surface  of  the  crystalline  lens.  . .  10.20  mm. 

Radius  of  the  posterior  surface  of  the  lens 6.17  mm. 

Index  of  refraction  of  the  air i 

Index  of  the  cornea 1-337 

Index  of  the  aqueous  humor 1-3365 

Index  of  the  lens  (total  index) 1.42 

Index  of  the  vitreous  humor \.ii6^ 


THE    EYE,    AND    THE   THEORY    OF   GAUSS.  73 

The  optic  system  is  as  follows : 

Q{  the  cornea  : 

Position  of  the  first  principal  point _  0. 1 3  mm. 

Position  of  the  second  principal  point. —  0.14  mm. 

Position  of  the  first  nodal  point 8,08  mm. 

Position  of  the  second  nodal  point 8.07  mm. 

Position  of  the  anterior  focus 24.53  "^n^- 

Position  of  the  posterior  focus 32.47  mm. 

Anterior  focal  distance 24.40  mm. 

Posterior  focal  distance 32.61  mm. 

Refracting  power 40.98  D. 

OPTIC    SYSTEM    OF    THE    CRYSTALLINE    LENS. 

Position  of  the  first  nodal  point 5.96  mm. 

Position  of  the  second  nodal  point 6.14  mm. 

Focal  distance  of  the  lens 62.46  mm. 

Refracting  power 16.01  D. 

Combining  these  two  systems  we  have  the  complete  optic  system 
of  the  eyeball. 

Position  of  the  first  principal  point 1.54  mm. 

Position  of  the  second  principal  point 1.86  mm. 

Position  of  the  first  nodal  point 7.30  mm. 

Position  of  the  second  nodal  point 7.62  mm. 

Position  of  the  anterior  focus —i^.^q  mm. 

Position  of  the  posterior  focus 24.75  "^ni- 

Anterior  focal  distance i/.i  3  mm- 

Posterior  focal  distance 22.89  ^n"^- 

Refracting  power 58.38  D, 

It  will  be  noticed  that  the  cornea  is  two  and  one  half  times  as  re- 
fractive as  the  crystalline  lens.  The  sum  of  the  refracting  power  of 
the  dioptric  surfaces  of  the  eyeball  is  not  far  from  being  equal  to  the 
refracting  power  of  the  eye,  because  the  nodal  points  of  the  cornea 
and  of  the  lens  are  very  close  together.  The  refracting  power  of  the 
eye  would  be  exactly  equal  to  the  sum  of  the  refracting  power  of  its 


74  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

dioptric  surfaces  if  the  anterior  principal  point  of  the  lens  coincided 
with  the  posterior  nodal  point  of  the  cornea. 
In  the  formula : 

d  would  then  equal  F^  +  F{'  which  gives 

F  F" 
F  =  _1J1_L_ 
^  1      /T"  -\-  F' 

or  i//^'  =  i/^/+i//^i". 

REFRACTIVE    POWER    OF    EACH    OF   THE    DIOPTRIC    SURFACES   OF    EYEBALL. 
ACCORDING    TO    TSCHERNING. 

Anterior  surface  of  cornea +  47.24  D, 

Posterior  surface  of  cornea  (usually  neglected) —    4.73  D. 

Anterior  surface  of  crystalline  lens +    6. 1 3  D. 

Posterior  surface  of  crystalline  lens +    9.53  D. 

Total +  58.1715^ 

The  theory  of  Gauss  assumes  that  the  aperture  of  the  optic  system 
is  small.  In  optical  instruments  an  aperture  of  ten  or  twelve  degrees 
is  considered  the  limit  in  size,  while  in  the  eye,  the  pupil,  being 
about  4  mm.,  gives  an  aperture  to  the  cornea  of  twenty  degrees. 
We  do  not  see  the  pupil  in  its  real  size  or  place,  but  a  magnified 
image  of  it  by  refraction  through  the  cornea.  It  is  apparently  moved 
forward  and  enlarged. 

Its  apparent  place  and  size  is  easily  determined.  We  can  deter- 
mine its  apparent  place  by  means  of  the  following  formula  : 

To  findy^,  we  give  to  the  remaining  quantities  their  values  as  de- 
duced from  the  cornea  of  the  simplified  eye.  (/^i  =  24 ;  7^  =  32, 
/2  =  3.6,  distance  between  cornea  and  iris.)    fi,  is  then  found  to  be 


THE   EYE,    AND   THE   THEORY   OF   GAUSS.  75 

equal  to  —  3.04  mm.  Suppose  that  the  real  size  of  the  pupil  is  4 
mm.,  its  apparent  size  is  4.5  mm.,  as  found  by  the  following  formula: 

110  =  FID 

O,  4  mm.  ;  F,  32  mm.  ;  D,  3.6  —  32  =  —  28.4  mm. ;  therefore 

^=^  =  4.5  mm. 

The  pupil  appears  therefore  to  be  moved  forward  by  about  .5  mm.^ 
and  to  be  enlarged  by  about  the  same  amount. 

Tscherning  applied  the  name  of  apparent  iris  and  apparent  pupil 
to  these  images  of  the  real  iris  and  pupil  as  seen  through  the  cornea. 
If  the  iris  and  the  pupil  could  be  viewed  by  eye  from  behind  the  eye- 
ball through  the  vitreous,  it  would  appear  .1  mm.  further  back  than 
it  really  is  and  enlarged  about  .2  mm.  Rays  coming  from  a  point  in 
the  real  pupil  would  proceed  into  the  vitreous  as  if  they  came  from 
a  point  in  the  crystalline  image  of  the  pupil.  If  the  corneal  and  the 
crystalline  images  of  the  pupil  be  constructed,  we  would  then  know 
that  a  ray  of  light  that  passed  through  a  certain  point  of  the  appar- 
ent corneal  pupil,  would  after  refraction  by  the  lens  pass  through  the 
same  point  in  the  crystalline  apparent  pupil.  Light  that  enters  the 
eye  is  limited  by  the  apparent  pupil,  in  its  passage  between  the  cor- 
nea and  the  lens,  by  the  real  pupil,  and  in  the  vitreous  by  the 
crystalline  image  of  the  pupil.  There  are  analogous  phenom- 
ena in  optical  instruments,  wherever  a  diaphragm  is  between  two 
lenses.  Abbe  proposes  the  names  of  pupil  of  entrance  and  pupil 
of  exit  for  the  images  of  the  diaphragm.  For  further  considera- 
tion of  the  subject  the  reader  is  referred  to  works  of  Helmholtz 
or  Tscherning. 

Accepting  the  theory  of  cardinal  points,  Bonders,  Listing  and 
Helmholtz  constructed  schematic  eyes.  The  data  in  the  eye  of 
Helmholtz  are  as  follows  : 


76  THE    EYE,    ITS    REFRACTION   AND    DISEASES. 

Refraction  index  of  air I 

Of  cornea  and  aqueous  humor 1-3365 

Of  the  lens I-437I 

Of  the  vitreous  humor 1-3365 

Radius  of  cornea 7.829  mm. 

Of  the  anterior  surface  of  the  lens 10  mm. 

Of  the  posterior  surface  of  the  lens 6  mm. 

Distance  of  the  apex  of  the  cornea  from  the  lens 3.6  mm. 

Thickness  of  the  lens 3.6  mm. 

The  position  of  the  cardinal  points  in  such  a  schematic  eye  are  as 
follows : 

/^i,  first  focal  point  is  13.745  mm.  in  front  of  the  anterior  surface 
of  the  cornea. 

/^,  posterior  focal  point,  15.689  mm.  back  of  the  lens. 

H',  first  principal  point,  1.753  "^"^-  back  of  the  posterior  surface 
of  the  cornea. 

H",  posterior  principal  point,  2.106  mm.  behind  the  cornea. 

N\  first  nodal  point,  6.968  mm.  behind  the  apex  of  the  cornea. 

N",  second  or  posterior  nodal  point,  7.321  mm.  behind  the  apex 
of  the  cornea. 

The  anterior  focal  distance  of  this  schematic  eye  i^  15.494  mm., 
and  the  posterior,  20.713  mm.  When  the  eye  is  adjusted  for  near 
vision,  the  relation  of  these  cardinal  points  is  changed  on  account  of 
the  change  in  the  curvature  of  the  lens.  Listing  and  Donders  fur- 
ther simplified  the  schematic  eye,  by  substituting  for  the  refracting 
system  a  single  refracting  surface,  bounded  anteriorly  by  the  air 
and  posteriorly  by  the  aqueous  or  vitreous  humor  as  both  have 
practically  the  same  index  of  refraction.  In  this  reduced  eye  the 
anterior  principal  and  the  anterior  nodal  points  may  be  disregarded 
without  introducing  any  error  into  the  determination  of  the  size  of 
the  retinal  image.  These  points  may  be  neglected  as  the  distance 
separating  them  is  so  minute  (.39  mm.).  There  is  then  in  the  re- 
duced eye  one  principal  and  one  nodal  point,  the  latter  being  the 
center  of  curvature  of  a  single  refracting  surface. 


THE    EYE,    AND   THE   THEORY   OF   GAUSS.  77 

The  dimensions  of  the  reduced  eye  of  Listing  are  as  follows: 
From  the  anterior  surface  to  the  principal  point,  2.106  mm.;  to  the 
nodal  point,  7.321  mm.  The  anterior  focal  distance  is  15.498  mm., 
20.783  mm.  The  radius  of  curvature  of  the  refracting  surface  is  5.215 
mm.,  the  index  of  refraction  is  1.3365  mm.,  the  same  as  that  of  the 
aqueous  humor. 

The  reduced  eye  of  Donders  departed  a  litde  more  from  the  con- 
ditions present  in  the  natural  eye.  Its  axial  length  is  20  mm.;  the 
refracting  surface  has  a  curvature  of  5  mm.  radius  ;  the  nodal  point 
in  consequence  is  5  mm.  behind  the  apex  of  the  refracting  surface ; 
and  15  mm.  in  front  of  the  retina.  The  index  of  the  eye  is  that 
of  the  aqueous  humor.  The  principal  focal  point  of  the  normal 
human  eye  amounts  to  about  22  mm.,  but  calculations  in  regard  to 
the  size  of  retinal  images,  diffusion  circles,  etc.,  in  the  reduced  sche- 
matic eye  give  results  approximating  closely  those  found  for  the  real 
eye. 

One  often  wishes  to  measure  the  size  of  a  retinal  image  or  of  a 
lesion  in  the  fundus  of  the  eye. 

To  Ascertain  the  Size  of  the  Retinal  Image.  —  As  has  been  shown 
the  size  of  an  image  formed  by  a  refracting  surface  is  to  the  size  of 
the  object  as  the  distance  of  the  image  from  the  nodal  point  is  to  the 
distance  of  the  object  from  the  nodal  point.  In  the  eye  (reduced  eye 
of  Donders)  the  distance  of  the  nodal  point  from  the  retina,  is  15 
mm.,  and  from  the  cornea  5  mm.  If  an  object  is  situated  at  2  m. 
distance  the  size  of  its  retinal  image  is  15/2,000  of  the  size  of  the 
object.  The  5  mm.,  the  distance  of  the  nodal  point  to  the  cornea, 
may  be  neglected  in  these  calculations.  The  angle  formed  at  the 
nodal  point  of  the  eye  by  lines  drawn  from  the  extremities  of  the 
object,  is  called  the  visual  angle. 

Angle  V  is  the  visual  angle ;  N,  the  nodal  point ;  O,  the  object. 
This  nodal  point  in  the  normal  human  eyeball  lies  a  little  posterior 
to  the  posterior  pole  of  the  crystalline  lens. 

Distance  of  V  to  N=  7.321  mm.;  V  to  P,  3.6  mm.;  P'  to  P,  3.6 
mm.;  F to  P',  7.2  mm.;  Z*' to  iV,  .1  mm.;  AT?  =  15.498  mm.    .1  mm. 


78 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


can  be  neglected,  making  the  nodal  point  coincide  with  the  posterior 
pole  of  the  crystalline  lens.     The  lens  of  the  eye  is  often  4  mm. 


thick,  so  under  such  a  condition,  the  nodal  point  is  dislocated  .3  mm. 
anterior  to  the  posterior  pole  of  the  crystalline  lens. 


CHAPTER   V 


VISUAL    ACUITY    AND    ACCOMMODATION 

The  apparent  size  of  an  object  depends  upon  the  size  of  the 
angle  of  vision  subtended  by  the  object.  The  further  from  the  eye 
an  object  is  viewed  the  smaller  does  it  appear,  as  the  further  away 
an  object  is  the  smaller  the  visual  angle.  Objects  appear  smaller  to 
the  hyperope  and  larger  to  the  myope  than  to  the  emmetrope,  as  the 
area  of  retinal  stimulation  is  smaller  and  larger  respectively,  than  in 
the  emmetropic  eye.     See  figure. 


Let  E  be  an  eye  ;  H,  E  and  M,  the  positions  of  the  hyperopic, 
emmetropic  and  myopic  retinas  respectively.  N  is  the  nodal  point 
of  the  eye.  a  and  b  are  two  objects  at  different  distances  from  the 
eye,  each  subtending  the  same  visual  angle,  as  lines  drawn  from  the 
extremities  of  each  form  the  same  angle  at  N.  If  a  without  change 
of  size  was  moved  to  the  position  of  b,  it  would  appear  smaller, 
as  it  would  then  subtend  a  smaller  ang-le.  The  extent  of  the  retinal 
impression  in  each  is  xy,  x'y'  and  x"y'\  for  a  or  b,  and  for  a  in  the 
position  b,  xz,  x'z'  and  x"z'\  respectively.  The  retinal  image  is  em- 
braced between  the  sides  of  the  visual  angle,  that  is  between  a  and 
b.  An  object  to  be  visible  to  the  unaided  eye  must  subtend  a  visual 
angle  of  i'.  If  its  shape  is  to  be  discerned  it  must  subtend  an  angle 
of  5'  at  the  nodal  point  of  the  eye.  This  is  called  the  limit  visual 
angle.     If  an  object  is  smaller  than  this  its  retinal  image  will  not 

79 


8o  THE    EYE,    ITS    REFRACTION   AND    DISEASES. 

embrace  one  percipient  element  of  the  retina.  A  distant  star  or  a 
point  of  light  is  visible,  even  if  it  subtends  a  much  smaller  angle  than 
i',  but  if  two  stars  or  points  are  to.  be  discerned  as  two,  they  must 
be  separate  at  least  60"  or  i',  otherwise  the  image  of  each  will  fall 
upon  and  influence  the  same  percipient  retinal  element,  and  the 
stimulus  will  be  carried  to  the  brain  as  one.  For  two  objects  to  be 
recognized  separately,  they  must  at  least  stimulate  two  retinal  ele- 
ments. 

An  object  nearer  than  twenty  feet  cannot  be  seen  clearly  by  the 
normal  eye  even  if  the  object  does  subtend  the  proper  size  visual 
angle,  without  the  use  of  accommodation.  It  is  not  only  necessary 
that  an  object  to  be  seen  clearly  should  subtend  a  visual  angle  of  5', 
but  rays  of  light  from  each  point  in  the  object  must  be  brought  to 
an  accurate  focus  upon  the  retina  to  form  the  corresponding  point  in 
the  retinal  picture. 

If  the  object  is  at  or  beyond  twenty  feet  from  the  eye,  the  light 
comes  to  the  eye  in  practically  parallel  paths,  and  the  focusing  is  ac- 
curate without  the  aid  of  accommodation,  as  the  emmetropic  eye  is 
adjusted  for  parallel  rays  of  light,  its  retina  lying  at  the  principal  focus 
of  its  dioptric  system.  The  angle  that  an  object  subtends  at  the 
greatest  distance  at  which  it  is  visible  represents  the  rpaximum  acute 
ness  of  vision.  An  object  twice  the  size  could  be  seen  at  twice  the 
distance  and  vice  versa.  The  size  of  an  object  denoting  acuteness 
of  vision  is  proportional  to  the  distance. 

Snellen  devised  a  series  of  letters  subtending  an  angle  of  5'.  The 
letters  were  formed  of  strokes  in  width  one  fifth  the  size  of  the  entire 
letter,  consequently  each  limb  of  the  letter  at  the  distance  it  was  de- 
signed to  be  read  subtended  an  angle  of  i',  while  the  whole  letter 
subtended  an  angle  of  5'.  The  openings  or  interspaces  of  the  letter 
were  likewise  made  to  conform  to  this  same  standard.  The  relation 
of  the  size  of  a  letter  to  the  distance  it  should  be  read  by  the  normal 
eye  is  twice  the  tangent  of 'half  the  angle  of  5'  =  .001425. 

In  the  diagram  let  A^be  the  nodal  point  of  an  eye  ;  AB,  an  object 
at  the  distance  D  from  A^.     In  either  position  of  AB,  the  size  of  its 


VISUAL  ACUITY   AND   ACCOMMODATION. 


8i 


retinal  image  will  be  i.     Let  angle    F=  5',  the  limit  visual  angle. 
Draw  line  NO,  and  let  it  bisect  the  angle  Fand  the  line  AB. 

AO=  OB.      In  triangle  ANO,  tan  F/ 2  =  ^ 01  NO.     A0  =  tan 
VI2XD.     A0  =  AB/ 2,  ergo  :  AB  =  2  tan  Vj 2  X  D,  or  expressing 
the  object  as  O  and  the  distance  of 
it  from  the  eye  as  D,  the  formula 
to  ascertain  the  size  of  the  object 
becomes : 

6^  =  2  tan  2^°  XZ^. 

Twice  the  tan  of  2^/^°  =  .001425, 
ergo  :  O  =  .001425  V. 

The  size  of  a  letter  to  be  seen 
at  a  given  distance  is  then  ascertained  by  multiplying  .001425  by 
the  distance  expressed  in  millimeters.  At  a  distance  of  one  meter 
the  size  of  a  standard  letter  is  1.42  mm.  (.001425  X  1,000  mm.),  and 
a  letter  to  be  read  by  a  normal  eye  at  six  meters  to  express  visual 
acuity  must  be  (.001425  X  6,000  mm.)  8.5  mm.  in  size. 

The  size  of  the  retinal  image  of  a  standard  letter  at  six  meters  is 
15/6,000  of  8.5  mm.  or  .02124  mm.  (The  size  of  an  object  and  its 
image  are  to  each  other  as  their  respective  distances  from  the  lens.) 
Some  people  have  better  vision  than  that  expressed  by  a  5'  stand- 
ard, so  letters  subtending  an  angle  of  only  4'  at  a  given  distance 
have  been  constructed.  The  retinal  image  of  the  limbs  of  such  a 
letter  is  four  fifths  of  the  size  of  those  of  the  5'  standard  letter,  that 
is,  .0034  mm.  The  perceptive  elements  of  the  central  part  of  the 
retina  vary  in  size  from  .0032  to  .0036  mm.,  showing  a  very  close  re- 
lation between  the  size  of  the  cones  of  the  retina  and  acute  vision. 
There  are  many  copies  of  test-letters  to  be  had  that  do  not  conform 
closely  to  the  5'  standard.  Perhaps  the  very  best  set  of  letters  is  that 
devised  by  Dr.  Randall.  The  card  has  regular  and  practical  intervals 
and  closest  practical  adherence  to  the  i -minute  parts  and  interspaces. 

Landolt  has  lately  advocated  the  use  of  circles  the  thickness  of 
Snellen's  letters,  each  broken  at  some  point  in  its  contour  by  a  space 


82 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


equal  to  the  thickness  of  the  circle.  The  space  in  each  case  sub- 
tends an  angle  of  one  minute  at  the  distance  the  character  is  de- 
signed to  be  read,  and  visual  acuity  is  expressed  by  a  fraction  with 
the  distance  of  the  patient  from  the  test-card  for  the  numerator  and 
the  width  of  the  gap  in  the  circles  of  the  line  read  for  the  denomi- 
nator. The  advantages  claimed  for  these  characters  are  that  they 
can  be  made  to  conform  to  the  one-minute  standard ;  that  they  may 


O  E 

D  r  c 

T  O  L 

C  E  D  T 

O  F  C  L  D 

E  c  T  o  r 

D  E  C  Z.  O 

I  o  r  9  T  o 

a  c  T  o  r  s  L 


B    F 

N    H 


be  used  for  those  that  read  and  illiterates  alike,  and  that  they  are 
not  easily  memorized.  In  reading  them  the  patient  tells  in  each  case 
in  which  direction  the  circle  is  open. 

The  black  card  with  white  letters  is  that  devised  by  Dr.  Gould. 
It  is  claimed  that  upon  this  card  patients  can  usually  read  one  or  two 
lines  better  than  upon  the  card  with  black  letters,  and  that  the  black 
background  is  restful  to  the  eyes  of  the  patient,  in  consequence  of 
which  he  does  not  so  quickly  tire.  The  writer  has  not  found  this 
the  case.  The  white  letters  on  the  black  background  are  certainly 
not  as  well  seen  as  the  black  letters  on  the  white  card  by  artificial 


VISUAL  ACUITY   AND   ACCOMMODATION. 


83 


light.  An  old  card  is  better  to  use  if  one  is  compelled  to  use  artifi- 
cial light  in  refraction  work,  as  the  polish  of  the  surface  of  a  new 
card  dazzles  the  eye  of  the  patient  and  the  white  background  appears 
to  flow  over  into  the  letters,  obscuring  their  edges.  The  white  let- 
ters on  the  black  card  seem  enlarged,  as  they  make  a  very  vivid  im- 
pression on  the  retina  and  irradiation  causes  the  letters  to  appear 
to  flow  over  into  the  background.  The  letters,  while  appearing  en- 
larged, are  not  read  the  more  easily,  as  their  edges  are  blurred  by 


E 

lU 

-E 

llJ 

3 

-  3 

m 

E 

-     E 

111 

3 

3  PI 

3 

m  E 

-     E  U  a  PI  E  III  3 

a 

r 

0  X 

& 

fX  w 

jC 

•    m  X 

je 

V  fS   t 

w  a 

A  r  £  «  J 

IT  n  r 



3  4 

the  irradiation.  (A  white  object  on  a  black  background  appears 
larger  than  a  black  object  of  the  same  size  on  a  white  ground,  due 
to  irradiation.) 

No.  3  is  a  test-card  to  be  used  for  illiterates.  The  letter  E  is 
turned  in  different  directions  and  is  made  according  to  the  scale  of 
5'.  The  patient,  instead  of  reading  the  letters,  tells  in  which  direc- 
tions the  strokes  of  the  characters  point,  whether  to  the  right  or  to 
the  left,  up  or  down.  Card  4  is  made  in  German  for  those  who  do 
not  read  English.  There  is  also  to  be  had  a  card  with  Hebrew  char- 
acters. The  picture  cards  intended  for  children  too  young  to  read 
are  not  reliable  as  it  is  almost  impossible  to  make  the  pictures  to 
conform  with  the  usual  standard  of  acute  vision.     If  the  examiner  is 


o 

eo  rt:t.t 


84  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

not  familiar  with  the  German  and  Hebrew  characters  he  may  hold  in 
his  hand  a  small  tally  card  upon  which  the  names  of  the  characters 
are  written  in  English  and  thus  keep  himself  straight. 

Dr.  Williams  has  devised  some  test-cards  to  be  used  for  testing 
the  visual  acuity  of  railroad  employees,  the  characters  being  made  to 
represent  semaphores  when  placed  in  different  positions,  which  cor- 
respond, when  seen  at  a  distance  of  twenty  feet,  to  the  apparent  size 
of  the  semaphore  arm  when  seen  at  a  distance  of  2,600  feet.  The 
cards  contain  three  different  arrangements  of  letters  for  each  of  the 
standard  distances,  which  avoids  the  difficulty  caused  by  the  patient 
memorizing  the  letters.  The  card  shown  in  cut  is  designed  to  be 
seen  at  a  distance  of  twenty  feet. 

The  upper  arm  of  semaphore  is  for  the  near  track  and  the  lower 
one  for  the  off  track.     Where  the  arm  forms  a  right  angle  with  the 

pole,  it  implies  that  that  section  of 
track  is  blocked  and  when  lowered 
that  the  road  is  clear. 

Visual  acuity  is  expressed  by  a 
fraction  the  numerator  of  which 
denotes  the  distance  at  which  a 
certain  letter  or  line  of  letters  is  read  and  the  denominator  the  dis- 
tance at  which  the  letter  or  line  should  be  read  by  the  normal  eye, 
or  putting  it  another  way :  The  numerator  of  the  fraction  denotes 
the  distance  of  the  patient  from  the  test  card,  and  the  denominator 
the  number  of  the  line  of  letters  read  at  that  distance. 

The  lines  on  the  test-card  are  numbered  either  above  or  at  the  side 
by  figures  denoting  in  feet  or  meters  the  distance  at  which  the  par- 
ticular lines  are  designed  to  be  read.  If  the  refractionist  has  the 
space  it  is  always  better  to  test  the  eyes  from  a  distance  of  6  m.  or 
20',  as  from  that  distance  practically  no  accommodation  is  needed  by 
the  normal  eye.  If  a  closer  distance  has  to  be  selected  than  6  m., 
the  use  of  accommodation  is  stimulated  which  is  apt  to  lead  into  error. 
If  a  patient  is  sitting  at  20'  or  6  m.,  and  only  reads  the  line  designed 
to  be  read  at  a  distance  of  100'  or  30  m.,  his  vision  is  K(from  visus, 


F  r  fc  K  h 


E.   B.  MEYROWITZ,  N.  Y. 


VISUAL  ACUITY   AND   ACCOMMODATION.  85 

the  Latin  of  sight)  =  20/  100,  or  by  the  metric  system  6/30.  If  the 
vision  is  better  than  normal  it  is  expressed  by  a  fraction  in  the  same 
way,  save  in  such  a  case  the  numerator  will  be  greater  than  the  de- 
nominator. Thus  :  At  20'  a  man  sees  that  designed  to  be  read  only 
at  10',  his  vision  is  then  20/10  and  so  on.  The  fraction  expressing 
the  visual  acuity  is  not  reduced  to  its  lowest  terms,  but  left  unreduced 
so  that  one  seeing  it  may  know  at  what  distance  the  vision  was  tested. 
The  Germans  use  S  instead  of  V  to  denote  the  visual  acuity  (Sehs- 
scharfe,  meaning  visual  acuity). 

In  1 89 1,  Guillery  proposed  to  measure  visual  acuity  by  the  distance 
at  which  a  black  spot  on  a  white  ground  could  be  distinguished.  He 
found  that  a  black  point  seen  under  an  angle  of  50"  corresponds  to 
normal  visual  acuity.  At  five  meters  the  point  would  have  to  be  1,2 
mm.  in  diameter.  The  dots  are  numbered  according  to  the  size,  no. 
2  being  twice  the  diameter  of  no.  i,  and  so  on.  If  a  patient  at  a  given 
distance  saw  no.  2,  when  he  should  have  been  able  to  see  no.  i,  his 
vision  is  one  half  and  so  on.  Javal  has  constructed  a  similar  test 
using  small  squares  so  that  the  area  of  each  square  is  always  double 
that  of  the  preceding  square.  The  diagonal  of  one  square  is  taken 
to  be  the  side  of  the  next  succeeding  square.     If  the  side  is  2,  the 

diagonal  is  

l/22+22  =  -/8: 

Test-Type  for  Near  Vision. — Those  generally  in  use  for  this  are 
Jaeger's  or  Snellen's.  The  latter  are  graduated  that  each  should  be 
read  at  the  distance  for  which  it  is  marked.  The  smallest  should  be 
seen  at  a  distance  of  50  cm.,  and  the  largest  at  4  m.  (i 2  feet).  These 
types  are  given  to  the  patient  and  we  note  the  smallest  that  he  can 
read  and  also  the  nearest  and  furthest  point  from  the  eyes  at  which 
he  can  read  it.  The  small  types  are  chiefly  used  to  test  the  accom- 
modation, but  they  are  also  of  service  in  testing  for  myopia  or  near- 
sightedness. 

Dr.  Ziegler's  arrangement  of  Jaeger's  near  test-types  is  a  good 
one.     Each  paragraph  is  numbered  from   i  to  20,  and  the  dioptric 


86  THE   EYE.    ITS   REFRACTION   AND    DISEASES. 

equivalent  is  placed  along  the  margins.     A  bar  of  notes  for  testing 
musicians  and  some  symbols  for  the  seamstress  are  appended. 

The  visual  acuity  falls  off  as  soon  as  the  object  is  moved  away  from 
the  fovea,  to  one  eighth  or  one  tenth.  To  estimate  peripheral  visual 
acuity,  Bjerrum  repeats  the  perimetric  examination,  using  smaller  and 
smaller  objects.  He  uses  a  distance  of  2  m.,  placing  the  patient  in 
front  of  a  large  black  curtain  ;  the  objects  used  are  small  ivory  discs 
of  various  sizes  fixed  on  black  rods  i  m.  in  length.  It  is  said  that 
in  cases  of  optic  nerve  atrophy,  the  peripheral  visual  acuity  is  often 
diminished  before  the  visual  field  has  become  curtailed.  The  limits 
of  the  visual  field  according  to  Bjerrum  are  as  follows  : 

With  a  3-mm.  disc  :  35,  outside  ;  30,  inside  ;  30,  below  ;  25,  above. 
With  a  6-mm.  disc  :   50,  outside  ;  40,  inside  ;  40,  below  ;  35,  above. 

If  we  draw  several  dots  on  a  sheet  of  paper  and  fix  one  of  them  for 
some  time  we  will  notice  that  now  one  and  now  another  of  the  sur- 
rounding dots  will  disappear  from  view,  to  reappear  after  a  little, 
generally  if  the  eyes  are  moved  or  after  winking.  This  is  called 
Troxler's  Phenomenon.  The  color  of  the  ground  as  well  as  that  of 
the  spots  plays  no  part.  One  must  guard  against  an  error  in  peri- 
metric examination,  due  to  this  phenomenon.  No  explanation  is 
offered  as  to  the  cause  of  this  phenomenon. 

Accommodation. — Accommodation  is  the  change  in  the  refraction 
of  an  eye,  due  to  an  increased  convexity,  and  hence  an  increase  in 
strength  of  the  crystalline  lens,  due  to  the  action  of  the  ciliary  muscle, 
whenever  the  eye  looks  from  a  distant  to  a  near  object.  The  nor- 
mally refracting  eye  only  needs  accommodation  when  it  fixes  an 
object  nearer  than  20  feet  or  6  m.,  while  the  hyperopic  eyeball  needs 
it  for  distance  as  well  if  it  is  to  receive  well-focused  retinal  pictures. 
Accommodation  does  the  same  for  an  eye  that  the  placing  of  a  con- 
vex spherical  lens  in  front  of  it  would  do,  that  is  the  increased  con- 
vexity of  the  dioptric  media  shortens  foci.  The  refraction  of  an  eye 
when  at  rest,  that  is,  without  any  effort  on  the  part  of  the  ciliary 
muscle,  is  spoken  of  as  its  static  refraction,  and  the  eye  is  adjusted  so 


Aeo.  ShttrteTi'NigiF«oal  Distaacfis 


VISUAL   ACUITY   AND   ACCOMMODATION.  87 

that  rays  proceeding  from  a  distant  point,  called  its  far-point,  come  to 
a  focus  upon  the  retina.  When  the  eye  is  using  all  of  its  available 
accommodation  it  is  adjusted  for  its  near-point.  The  refraction  of 
the  eye  when  adjusted  for  its  near-point  is  called  the  dynamic  refrac- 
tion. The  entire  amount  (amplitude)  of  accommodation  of  an  eye  is 
employed  as  the  eye  passes  from  the  far-point  (denoted  by  R.)  to  its 
near-point  (denoted  by  pp.  or  by  p.). 

The  far-point  is  spoken  of  as  the  punctum  remotum,  and  the  near 
point  as  the  punctum  proximum.     The  need  of  accommodation  is  at 
once  apparent  when  we  recall  that 
the  normal  eye  is  adjusted  when  at 
rest  for  parallel  rays  of  light  only, 
and  that  from  near  objects  the  light 
proceeds  from  every  point  in  the  ob- 
ject in  diverging  paths,  and  that  di- 
verging  rays  of  light   are   focused 
posterior  to   parallel  rays  of  light, 
so  that  the  image  of  near  objects  would  be  blurred,  unless  the  focal 
length  of  the  dioptric  system  of  the  eyeball  is  shortened. 

In  the  figure  E  represents  an  emmetropic  or  normally  refracting 
eye.  Rays  i  and  2  are  parallel,  coming  to  it  from  a  distance  of  20  feet 
or  more,  and  are  focused  upon  the  retina  without  accommodation  as 
the  emmetropic  eye  is  adjusted  when  at  rest  for  focusing  parallel 
rays  (plane  waves)  of  light.  Rays  2  and  3  come  to  the  eye  divergent  ; 
as  they  emanate  from  a  near  point,  they  are  not  brought  to  a  focus  as 
the  retina  of  the  eye  intercepts  them  ;  if  they  continued  they  would 
come  to  a  focus  at  the  point  F' ,  because  divergent  rays  of  light  are 
focused  posterior  to  parallel  rays.  The  circle  of  illumination  on  the 
retina  embraced  by  the  rays  that  emanate  from  the  point  N,  is  called 
a  diffusion  circle.  In  order  that  the  point  N  may  be  seen  distinctly 
the  focus  of  it  must  lie  upon  the  retina  of  the  eye.  This  is  accom- 
plished by  the  lens  of  the  eye  becoming  stronger  through  accommo- 
dation, which  shortens  the  focal  distance  of  the  eyeball,  and  brings 
F'  up  to  F,  or  upon  the  retina. 


88 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


It  will  be  noticed  that  now  the  parallel  rays  of  light  have  been 
brought  to  a  focus  anterior  to  the  retina  and  crossing  from  a  diffu- 
sion circle  upon  the  latter.  It  is  therefore  evident  that  an  eye 
cannot  be  adjusted  at  the  same  time  for  both  parallel  and  divergent 

rays  of  light  for  distant  and  near 
seeing.  It  is  not  difficult  to  calcu- 
late the  size  of  a  diffusion  circle  on 
the  retina.  If  the  diameter  of  the 
pupil  be  designated  by  /  (the 
smaller  the  pupil  the  smaller  the 
circle  of  diffusion);  its  distance  from  the  retina  by  a ;  and  the  distance 
of  the  principal  focus  of  the  eyeball  by  fl^;  we  have  the  following  for- 
mula to  ascertain  x,  the  diameter  of  the  diffusion  circle  : 


x=  p 


d 


d-\-  a 


In  triangles  pFd-\-  a,  and  xFd :   sides  p  and  x  are  to  each  other  as 


d-\-  a\?>X.o  d. 


xlp  =  djd+a,  or  x  =  dld  +  a  Xp. 


The  following  is  Listing's  table  of  the  size  of  diffusion  circles  in  the 
emmetropic  eye  of  objects  at  varying  distances  : 


Distance  of  Luminous  Point, 

Distance  of  Focus  Behind  the  Retina, 

Diameter  of  Diffusion  Circle, 

Meters, 

Millimeters. 

Millimeter. 

OO 

0 

0 

65 

0.005 

O.OOII 

25 

0.012 

0.0027 

12 

0.025 

0.0056 

6 

0.050 

O.OII2 

3 

O.IOO 

0.0222 

1.500 

0.200 

0.0443 

0.750 

0.40 

0.0825 

0.375 

0.80 

O.I616 

0.188 

1.60 

0.3122 

0.094 

3.20 

0.5678 

0.88 

342 

0.6486 

The   amplitude  or   the   amount  of  available   accommodation   is 
measured  by  the  strongest  convex  spherical  lens  with  which  the 


VISUAL   ACUITY   AND    ACCOMMODATION, 


89 


eye  can  see  as  well  with  as  without  when  adjusted  for  the  punctum 
proximum. 

One  begins  with  a  weak  convex  sphere  and  places  successively- 
stronger  and  stronger  lenses  before  the  eye,  until  the  vision  begins 
to  be  blurred  at  the  near  point  after  having  determined  the  position 
of  the  near-point  by  ascertaining  the  closest  distance  at  which  the 
finest  discernible  print  can  be  read  by  the  unaided  eye.  As  succes- 
sive strengths  of  lenses  are  added,  the  accommodation  each  time  a 
stronger  one  is  put  on  relaxes  a  little,  allowing  the  glass  lens  to  do 
the  work  for  it,  until  all  is  relaxed.  If  the  accommodation  was  not 
relaxed  each  time,  the  glass  lens  would  spoil  the  vision  by  bringing 
the  focus  anterior  to  the  retina,  that  is  the  eye  would  be  made  myopic. 
The  amount  of  accommodation  needed  by  the  emmetropic  eye  for 
any  given  distance  is  equal  to  the  lens  whose  focal  length  is  that 
distance.  Thus  :  For  i  m.  distance,  the  E.  needs  i  D.  of  accom- 
modation ;  or  according  to  the  inch  system,  as  i  m.  equals  40",  one 
fortieth  accommodation. 

Always  divide  the  distance  at  which  the  object  is  seen,  expressed 
in  cm,  into  100  cm.  (i   m.)  or  the  number  of  inches  at  which  the 
object  is  seen  into  40,  to  ascertain  the  number  of  diopters  of  accom- 
modation in  use  for  that  distance. 
This  is  evident  by  referring  to  the 
figure. 

Let  L  represent  the  lens  of  an 
emmetropic  eye  in  accommodation, 
for  the  point  O  at  i  m.  distant 
from  the  eye.  Portion  /'  is  the  in- 
crease of  strength  of  lens  caused  by  accommodation  ;  /,  the  strength 
of  the  lens  when  the  accommodation  is  relaxed,  or  when  the  eye  is 
at  rest.  The  light  from  O  comes  divergent  to  L.  Portion  /'  renders 
them  parallel  and  then  portion  /  focuses  them  upon  the  retina.  The 
strength  of  the  portion  /'  is  i  D.,  as  rays  of  light  emanating  from 
a  point  at  one  meter's  distance  are  rendered  parallel  by  a  i  D. 
lens.     How  much  accommodation  is   required  by  the  emmetropic 


90  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

eye  to  see  distinctly  an  object  lo  cm.,  50  cm.,  200  and  400  cm. 
away? 

100/10=  10  D.,  100/50  =  2  D.,  100/200  =  .50  D.,  100/400  =  .25  D. 

The  entire  amount  of  or  amplitude  of  accommodation  is  obtained 
by  the  following  formula  : 

Amount  of  _  refraction  of  the  eye  at  refraction  of  the  eye  at 
accommodation  the  near-point  the  far-point. 

or,  A=p-R, 

or,  as  it  is  sometimes  written 

A  =  D  —  S  (dynamic  —  static  refraction  of  the  eye). 

In  each  of  these  equations  the  respective  values  of  the  quantities 
on  the  right-hand  side  are  expressed  in  diopters.  R  is  the  point  for 
which  the  eye  is  focused  when  at  rest.  The  emmetropic  eye  is 
focused  when  at  rest  for  parallel  rays  of  light.  Parallel  rays  of  light 
only  come  from  a  distance  of  infinity,  therefore,  the  R  of  the  emme- 
tropic eye  lies  at  an  infinite  distance.  The  strength  of  a  lens  whose 
focal  length  is  infinity  is  o  D.,  that  is  it  is  no  lens  at  all.  How  is  it 
that  parallel  rays  of  light  come  to  the  eye  only  from  a  distance  of 
infinity  ?  When  it  was  stated  in  a  former  section  that  when  rays  of 
light  came  to  the  eye  from  a  distance  of  twenty  feet  or  beyond,  they 
may  be  regarded  as  parallel. 

Strictly  speaking,  rays  of  light  do  come  to  the  eye  diverging  from 
all  distances  short  of  infinity  ;  but  from  distances  beyond  20',  the  size 
of  diffusion  circles  on  the  retina  are  so  small  that  they  may  be  disre- 
garded, as  they  do  not  interfere  materially  with  the  sharpness  of  the 
retinal  images.  To  obtain  the  value  of  /,  Landolt's  ophthal-dynom- 
eter  is  useful.  A  screen  which  is  made  to  fit  a  candle  has  a  number 
of  perforations  in  it  arranged  in  a  row.  Attached  to  the  instrument 
there  is  a  tape  measure,  marked  in  centimeters  on  one  side  and  in 
the  equivalent  number  of  diopters  on  the  other.  The  patient  holds 
the  instrument  as  close  to  his  eyes  as  it  is  possible  to  see  the  per- 


VISUAL   ACUITY    AND   ACCOMMODATION. 


91 


forations  separately,  and  then  the  distance  from  the  eye  and  the 
amount  of  accommodation  in  use  for  that  distance  is  read  off  from  the 
tape-line.  The  patient  of  course  must  exert  all  his  effort  to  see  as 
close  by  as  possible  in  determining  the  value 
of  /.  The  value  of  p  is  then  influenced  to  a 
certain  extent  by  the  will  and  intelligence  of 
the  patient.  Theoretically  the  instillation  of 
eserin  sulphate  would  give  the  absolute  posi- 
tion of  the  near-point,  as  the  ciliary  muscle  is 
thrown  into  the  strongest  contraction  by  the 
drug.  The  value  of/  thus  obtained  would, 
however,  be  too  great  for  practical  purposes. 
Very  accurate  results  can  be  obtained  by  ascer- 
taining the  nearest  point  at  which  the  finest 
readable  print  can  be  distinctly  seen.  Or,  a 
number  of  black  dots  or  small  pin-holes  can 
be  made  in  a  card,  and  the  card  brought  closer 
and  closer  to  the  eyes  until  the  dots  or  perforations  are  seen  to  fuse 
into  one  continuous  line.  In  emmetropia  then  A  equals  the  dynamic 
refraction,  inasmuch  as  R  has  no  value  in  the  equation  A=  p  —  R. 

If  an  eye  emmetropic  or  made  so  by  spectacles  can  read  at  ten 
centimeters  the  finest  discernible  print,  the  amount  of  accommoda- 

.        10)100  T  •  1-1  •  n 1  •  1  •  V 

tion  IS  - — ^  In  myopia  and  m  hyperopia,  R  has  its  value  in  di- 
opters. The  myopic  eye  is  not  able  to  bring  parallel  rays  to  a  focus 
on  its  retina,  as  the  retina  of  the  myopic  eye  lies  posterior  to  the 
principal  focus  of  the  dioptric  system  of  the  eye.  In  order  that  such 
an  eye  may  receive  a  clear  retinal  picture  then,  it  is  necessary  that 
it  should  receive  divergent  rays  of  light,  as  divergent  rays  of  light 
are  focused  posterior  to  parallel  rays  of  light. 

Inasmuch  as  divergent  rays  of  light  only  come  to  the  eye  from  a 
finite  distance,  R  has  an  equivalent  finite  value.  The  point  situated 
in  front  of  the  myopic  eye  from  which  light  emanating  has  the  proper 
amount  of  divergence  to  be  focused  accurately  upon  the  retina  of  the 


92  THE  i:ye,  its  refraction  and  diseases. 

eye,  is  the  far-point  of  the  myopic  eye.  The  distance  of  this  far- 
point  expressed  in  diopters  is  the  value  of  R.  The  near-point  is 
ascertained  as  before  described.  Suppose  that  pis  at  lo  cm.,  and 
i^  at  I  m.,  then  A  =  p  —  7?  =  lo  D.  —  i  D.  =  9  D.  accommodation. 
The  near-point  assumed  for  emmetropia  and  for  myopia  in  the  above 
cases  is  the  same,  that  is  10  cm.,  and  from  the  formula  one  sees  that 
the  myope  of  i  D.  has  to  use  one  diopter  less  of  accommodation 
for  a  given  distance  than  does  the  emmetrope.  If  there  is  3  D.  of 
myopia,  then  3  D.  accommodation  less  are  needed,  and  so  on.  In 
hyperopia  the  value  of  R  is  negative  and  the  formula  for  the  ampli- 
tude of  accommodation  becomes:  A=  p  — {  — R)=  p-\r  R.  The 
H.  eye  is  adjusted  when  at  rest  for  only  converging  rays  of  light. 
Such  rays  have  only  a  virtual  focus,  a  point  behind  the  eyeball 
where  they  would  come  together  if  they  were  unrefracted  as  they 
passed  through  the  dioptric  media  of  the  eyeball.  Converging  rays 
are  found  only  in  nature  after  they  have  passed  through  a  convex 
lens.  The  strength  of  the  lens  that  will  impart  to  parallel  rays  of 
light  entering  it  the  proper  amount  of  convergence  so  that  they  will 
be  focused  upon  the  retain  of  the  hyperopic  eye  at  rest  is  the  value 
of  R.  Such  a  lens  is  spoken  of  as  correcting  the  hyperopia.  The 
sign  of  R  is  negative  as  it  lies  behind  the  eyeball. 


In  the  figure  the  hyperopic  eyeball  is  focused  for  the  converging 
rays  a'  and  b',  rendered  so  by  the  convex  lens  L,  acting  upon  paral- 
lel rays  a  and  b.  If  L  is  equal  to  2  D.,  R  is  equal  to  —  2  D.  lying 
posterior  to  the  eyeball  at  —  R,  where  the  rays  a'  and  b'  would  meet 
if  unrefracted  by  the  dioptric  media  of  the  eyeball.  If/  is  assumed 
to  be  equal  to  10  D.  then,  A=  10+  2  =  12D.     The  hyperopic  eye, 


VISUAL   ACUITY    AND    ACCOMMODATION.  93 

then  for  a  given  distance  needs  the  amount  of  accommodation  of 
the  emmetropic  eye  plus  the  amount  of  its  hyperopia. 

The  range  or  region  of  accommodation  is  the  space  lying  be- 
tween the  far-point  and  the  near-point.  The  extent  of  the  region 
of  accommodation  forms  no  estimate  of  the  amount  of  work  done 
by  the  ciliary  muscle. 

Compare  region  of  accommodation  ;  the  space  between  J^  and  />, 
with  the  amplitude  A,  in  the  above  cases  of  E.,  H.  of  2  D.,  and  M. 
of  2  D.     The  normal  near-point  in  emmetropia  lies  at  4-5  inches, 


A  -lOD 


A-18D 

H 


50cm.  -2D 


R— 2D 


or  10-12.5  cm,  from  the  eyes.  It  gradually  recedes  further  and 
further  from  the  eyes,  until  the  age  of  seventy-five  years,  when  it  lies 
at  an  infinite  distance. 

Bull  calls  that  region  of  accommodation  lying  between  the  puncta 
remota  of  the  principal  meridians  of  the  astigmatic  eyeball,  the 
remote  range  of  accommodation. 


CHAPTER   VI 

ACCOMMODATION    (CONTINUED) 

Mechanism. — The  eye  could  theoretically  alter  its  focus  or  accom- 
modate in  any  of  the  following  ways  :  {a)  By  increase  of  corneal 
curvature  ;  {b)  by  increase  of  curvature  of  the  crystalline  lens  ;  {c) 
by  elongation  of  the  eye-globe  ;  (</)  by  advance  of  the  crystalline 
lens  ;  {e)  by  the  contraction  of  the  pupil. 

Each  of  these  methods  has  had  its  adherents,  theory  (</)  is  im- 
possible from  the  anatomical  arrangement  of  the  crystalline  lens  sys- 
tem of  the  eyeball.  In  certain  lower  animals,  however,  the  lens  is 
drawn  nearer  the  retina  in  focusing  the  eye  for  distant  seeing. 

Even  if  the  crystalline  lens  could  advance  to  the  posterior  surface 
of  the  cornea  it  would  not  suffice  to  explain  any  considerable  amount 
of  accommodation.  Scheiner  was  the  first  to  discover  that  lookino- 
at  objects  through  a  pinhole  increased  their  distinctness,  but  the  con- 
traction of  the  pupil  does  not  answer  for  any  considerable  amount 
of  accommodation.  Young  was  the  first  to  discover  that  accommo- 
dation depended  upon  a  change  in  the  curvature  of  the  lens  of  the 
eye.  He  disproved  theories  {a)  and  {c)  by  experiments  upon  his 
own  eyes.  Young  decided  that  the  cornea  did  not  change  during 
the  accommodative  act  as  he  could  notice  no  change  in  the  size  or 
shape  of  the  corneal  catoptric  image,  but  a  decided  change  in  the 
image  when  he  made  only  feeble  pressure  upon  the  periphery  of  the 
cornea,  thus  altering  its  contour.  His  most  conclusive  experiment 
consisted  in  putting  his  eye  under  water.  He  took  a  weak  objective 
of  a  microscope  which  had  nearly  the  same  index  of  refraction  as  the 
cornea,  filled  the  tube  with  water,  and  placed  it  before  the  eye  also 
plunged  into  water.  The  effect  of  the  cornea  on  the  refraction  of 
the  eye  was  now  eliminated  as  it  was  surrounded  on  both  sides  by  a 
liquid  with  the  same  index  of  refraction.     The  cornea  was  replaced 

94 


ACCOMMODATION. 


95 


by  the  lens  of  the  objective.  Under  these  conditions  he  noticed  that 
the  accommodation  remained  intact.  He  also  disproved  the  fact  that 
accommodation  depended  upon  the  elongation  of  the  eyeball,  by 
measurements  made  upon  his  own  eye.  Young  had  very  prominent 
eyes,  so  he  was  enabled  to  perform  the  following  experiment. 

He  turned  his  eye  inwards  as  much  as  he  could,  and  applied  against 
its  anterior  surface  a  strong  iron  ring  ;  then  he  thrust  the  ring  of  a 
little  key  on  the  external  side  between  the  eyeball  and  the  bone  until 
the  phosphene  reached  the  fovea.  Placed  between  the  ring  and  the 
key  the  eyeball  could  not  elongate  during  accommodation.  If  accom- 
modation depended  upon  elongation  of  the  globe,  he  should  have 
found  it  abolished  or  see  the  phosphene  due  to  pressure  extend  over 
a  much  larger  surface.  The  accommodation  remained  unaltered  and 
the  size  of  the  phosphene  did  not  change.  In  Young's  day  the  ciliary 
muscle  had  not  been  discovered,  so  he  was  unable  to  account  for  the 
change  in  shape  of  the  crystalline  lens.  The  crystalline  lens  rests 
in  the  fossa  patellaris  on  the  anterior  surface  of  the  vitreous  body. 
It  is  enclosed  within  its  capsule  and  held  in  place  by  a  suspensory 
ligament,  which  passes  from  the  ciliary  processes  over  its  anterior 
surface.  (A  small  portion  passes  posteriorly,  to  fuse  with  the  capsule 
of  the  lens.)  The  suspensory  ligament  is  taut  during  the  passive 
condition  of  the  eye,  and  keeps  the  lens  compressed  beneath  it.  By 
the  contraction  of  the  ciliary  muscle  the  pressure  upon  the  lens  is 
lessened,  and  it  through  its  own  elasticity  becomes  more  convex, 
responding  almost  entirely  upon  its  anterior  surface.  At  the  same 
time  the  lens  becomes  thicker,  its  diameter  between  the  ciliary  bodies 
becomes  less.  As  a  proof  of  the  increased  convexity  of  the  crystal- 
line lens  during  accommodation,  the  experiments  of  Hensen  and 
Volckers  may  be  cited.  These  experiments  removed  a  part  of  the 
outer  tunic  of  the  eyeball  lying  over  the  ciliary  muscle,  in  the  cat, 
dog  and  monkey.  They  then  introduced  pins  through  the  sclerotic, 
so  that  the  point  of  one  should  rest  upon  the  anterior  surface  of  the 
lens  about  its  center,  and  another  upon  the  center  of  the  posterior 
surface.     Pins  were  also  introduced  into  the  chorioid.     On  electriz- 


96  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

ing  the  ciliary  muscle,  the  head  of  the  pin  resting  upon  the  anterior 
surface  of  the  lens  moved  backward,  showing  an  advance  of  the 
anterior  surface  of  the  lens.  The  head  of  the  pin  resting  upon  the 
posterior  of  the  lens  moved  forward — but  to  a  much  less  degree  than 
the  head  of  the  pin  upon  the  anterior  surface  of  the  lens  moved 
backward.  The  pins  in  the  chorioid  all  moved  backward,  showing 
that  the  chorioid  advanced  during  accommodation. 

Coccius  and  Hjort  in  cases  where  part  of  the  iris  was  absent,  no- 
ticed that  not  only  the  chlorioid,  but  also  the  retina,  advanced  during 
accommodation.  The  theory  that  the  iris  played  an  important  part 
in  the  act  of  accommodation  was  disproved  in  a  case  in  Von  Graefe's 
clinic  where  the  iris  was  entirely  removed  without  disturbing  in  the 
least  the  power  of  accommodation.  The  accommodation  is  also 
perfect  in  many  cases  of  congenital  absence  of  the  iris.  The  ciliary 
muscle  was  discovered  in  1846  by  Bowmann  and  Briicke,  working 
independently.  It  is  divided  into  three  portions,  namely :  A  meri- 
dional, horizontal,  or  radiating  portion  (Brijcke's  muscle)  ;  a  circular 
or  annular  (Miiller's)  and  a  diagonal  or  transitional  portion.  The 
circular  fibers,  or  those  of  Miiller,  are  the  most  important. 

In  eyes  that  accommodate  a  great  deal  they  are  excessively  devel- 
oped. The  ciliary  muscle  lies  upon  the  internal  surface.of  the  sclera, 
and  is  bounded  internally  by  the  ciliary  processes,  sixty  to  seventy 
in  number.  The  meridional  portion  of  the  ciliary  muscle  arises  from 
the  corneo-scleral  junction,  from  the  posterior  wall  of  Schlemm's 
canal  and  from  the  adjacent  sclera,  and  runs  posteriorly  to  be  at- 
tached to  the  anterior  extremity  of  the  chorioid  coat.  When  it  con- 
tracts it  draws  the  chorioid  forward,  and  through  the  vitreous  being 
interposed,  it  renders  the  posterior  surface  of  the  crystalline  lens 
stationary,  so  than  the  lens  cannot  recede  during  the  act  of  accom- 
modation. The  circular  fibers  surround  the  orifice  formed  by  the 
ciliary  processes  like  a  sphincter  muscle  in  any  other  locality  sur- 
rounds the  orifice  over  which  it  presides.  When  they  contract  they 
lessen  the  circumference  of  the  circle  over  which  they  have  control, 
and  thus  slacken  the  suspensory  ligament  of  the  lens.    The  diagonal 


ACCOMMODATION. 


97 


fibers  arise  along  with  the  horizontal  ones  and  run  diagonally  back- 
ward and  inward  towards  the  center  of  the  eyeball  and  are  attached 
to  the  suspensory  ligament,  which  is  drawn  forward  off  of  the  lens 
by  their  contraction. 

According  to  some  anatomists  these  latter  fibers  do  not  exist,  claim- 
ing them  to  be  transitions  between  the  circular  and  the  meridional. 
According  to  Heinrich  Miiller,  the  ciliary  processes  press  upon  the 
equator  of  the  lens  during  accommodation,  and  squeezing  upon  it  aid 
in  its  increased  convexity.  Accommodation  begins  to  fail  at  the  age 
of  ten  years  and  is  nil  at  the  age  of  seventy-five,  due  to  a  loss  of 
elasticity  of  the  lens,  caused  by  a  hardening  or  sclerosis  of  its  fibers. 

The  gradual  loss  of  elasticity  and  the  consequent  failure  to  re- 
spond to  the  contraction  of  the  ciliary  muscle  causes  the  near-point 
to  recede  pari  passu.  When  it  has  receded  beyond  the  point  of 
convenient  near  seeing  presbyopia  has  set  in.  The  normal  near- 
point  up  to  the  age  of  forty  years  lies 
at  4-5  in.  or  10— 12.5  cm.  from  the 
eyes.  If  it  lies  nearer  than  this,  myopia 
is  indicated  ;  and  if  further  ofif,  hyper- 
opia, that  is  in  individuals  under  the 
age  of  the  advent  of  presbyopia.  The 
accompanying  table  gives  the  range 
of  accommodation  at  different  ages 
according  to  Donders. 

With  the  contraction  of  the  ciliary 
muscle  there  is  an  associated  contraction  of  the  pupil,  due  partly  to 
the  rush  of  blood  from  the  ciliary  bodies  into  the  iris,  but  caused 
chiefly  by  a  stimulus  from  the  third  nerve,  in  the  floor  of  the  fourth 
ventricle,  to  the  sphincter  muscle  of  the  iris.  The  eyes  also  con- 
verge (turn  in  towards  the  nose)  during  the  act  of  accommodation. 

By  the  bulging  forward  of  the  anterior  surface  of  the  lens  the  cen- 
ter of  the  anterior  chamber  is  made  shallower,  while  at  its  periphery, 
its  depth  is  increased  by  the  retraction  of  the  root  of  the  iris  through 
contraction  of  the  more  deeply  seated  ciliary  muscle  fibers.     By  con- 
7 


98 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


traction  of  the  pupil  the  iris  is  made  more  taut  and  the  infiltration 
angle  between  the  iris  and  the  cornea  opened. 

The  retraction  of  the  periphery  of  the  iris  also  aids  in  widening  this 
space.  The  figure  below  shows  the  changes  that  take  place  in  each 
eyeball  during  accommodation. 

The  right  half  of  the  figure  represents  a  section  of  an  eyeball  with 
relaxed  ciliary  muscle  ;  the  left  half  one,  with  contracted  ciliary  muscle. 
It  will  be  noticed  that  accommodation  causes  the 
following  changes:  (i)  Lens  thicker,  and  equa- 
torial diameter  made  less  ;  the  change  in  shape 
of  lens  being  mostly  on  the  anterior  surface.  The 
ciliary  body- coming  in  contact  with  the  equator  of 
the  lens.  (2)  The  center  of  the  anterior  chamber 
made  shallower,  and  the  periphery  deeper.  (3) 
The  pupil  is  contracted  (and  in  regard  to  both 
eyes,  they  are  converged). 

The'  theory  of  accommodation  as  outlined  in  the 
preceding  paragraphs,  and  the  one  that  is  gener- 
ally accepted  is  that  of  Von  Helmholtz.  Tscherning  and  Young  dis- 
pute the  theory  that  accommodation  depends  upon  the  relaxation 
of  the  suspensory  ligament  of  the  lens,  due  to  contraction  of  the 
ciliary  muscle,  and  claim  that  the  periphery  of  the  lens  is  flattened  by 
contraction  of  the  ciliary  muscle,  and  that  the  curve  of  the  anterior 
surface  of  the  lens  assumes  a  hyperboloid  form  from  the  nearly  spher- 
ical form  that  it  has  during  a  state  of  rest.  The  change  in  the  shape 
of  the  lens  in  the  pupillary  area  is  seen  by  the  change  in  the  shape  of 
and  in  the  position  of  the  images  of  Purkinje,  which  was  discovered 
by  Max  Langenbeck  in  1849.  These  images  of  Purkinje  were  de- 
scribed by  the  scientist  whose  name  they  bear  at  the  beginning  of 
the  last  century.  They  are  catoptric,  that  is  formed  by  reflection  from 
the  anterior  surface  of  the  cornea  and  from  the  anterior  and  posterior 
surfaces  of  the  lens.  (There  are  three  other  catoptric  images  seen 
under  special  conditions  which  will  be  described  later.) 

If  a  lighted  candle  be  held  in  front  of  and  a  little  to  one  side  of  an 


ACCOMMODATION. 


99 


a.  Image  from  Ant.  Corneal  Sur, 

b.  "  II       ••       Lens 

c.  '■^  '■     Post       " 


l" 

61 

/Xtens 

X 

C^H 

ll 

J 

^ 

u 

■y 

^/Cornea 
I 

30\ 


eye  with  a  dilated  pupil,  three  images  of  the  light  are  seen  reflected 
from  the  eye,  provided  it  has  a  crystalline 
lens.  The  brightest  image  is  erect  and 
is  formed  by  reflection  from  the  cornea. 
The  largest  but  at  the  same  time  the  faint- 
est image  is  likewise  erect,  and  is  formed 
by  the  anterior  surface  of  the  lens.  The 
third  one  is  small,  but  bright  and  inverted, 

and  formed  by  reflection  from  the 
posterior  surface  of  the  lens. 

The  conditions  that  are  best 
suited  to  study  this  test  are  :  That 
the  room  should  be  dark  and  that 
the  light  be  placed  about  30  de- 
grees to  one  side  of  the  eye  and 
about  14  in.  distant. 

The  observer  should  place  him- 
self on  the  opposite  side  of  the 
eye  and  at  an  angle  of  30  degrees 
with  the  visual  axis  of  the  eye. 
The  images  in  the  pupil  will  then 
bear  the  relation  to  each  other 
shown  in  the  cut  no.  i.  If  the 
eye  now  adjusts  itself  for  a  nearer 
object,  without  changing  the  di- 
rection of  its  gaze,  the  images  will 
be  seen  to  bear  the  relation  shown 
in  figure  no.  2.  The  next  figure 
explains  how  the  change  in  the  position  of  the  catoptric  images  takes 
place  during  accommodation. 

During  the  accommodative  act  the  reflected  image  from  the  ante- 
rior surface  of  the  crystalline  lens  has  moved  towards  that  from  the 
anterior  surface  of  the  cornea. 

Light  falling  upon  the  vertex  of  the  cornea  at  O  forms  an  image  that 


Observer 
Eye 


lOO  THE   EYE,   ITS    REFRACTION   AND    DISEASES. 

appears  in  the  position  o(c,  when  projected  by  the  observer  upon  a  hor- 
izontal plane  xy.  The  relative  position  of  the  image  /  from  the  ver- 
tex of  the  anterior  crystalline  surface  is  not  altered  as  it  lies  in  the  hori- 
zontal plane.     L'  is  the  position  of  the  image  O",  formed  at  the  vertex 

of  the  posterior  crystalline  surface. 
When  the  anterior  surface  of  the 
crystalline  lens  bulges  forward  to  the 
position  of  a",  its  catoptric  image 
moves  to  the  point  L"  in  the  hori- 
zontal plane.  The  change  in  the 
shape  of  the  lens  necessitated  by 
accommodation  according  to  the 
theory  of  Von  Helmholtz,  is  shown  in  figure  a,  and  the  change  that 
takes  place  according  to  the  Tscherning  theory,  shown  in  figure  d. 

S  is  the  anterior  surface  of  the  lens  in  each  case,  and  S'  the  poste- 
rior surface.  The  dotted  lines  represent  the  lens  in  accommodation. 
Tscherning  believes  that  the  inner  portion  of  the  ciliary  muscle  has 
its  more  fixed  attachment  posteriorly  into  the  chorioid,  which  is  ren- 
dered stationary  by  the  tension  of  the  vitreous,  which  is  increased 
during  accommodation  due  to  a  backward  movement  of  the  lens. 
The  retraction  of  Miiller's  fibers  which  are  not  so  circularly  arranged 
as  was  formerly  supposed,  makes  traction  upon  the  suspensory  liga- 
ment, and  thus  produces  a  change  in  the  shape  of  the  crystalline  lens. 
The  particular  shape  that  the  lens  assumes  depends  in  part  upon 
the  arrangement  of  the  fibers.  The  deepening  of  the  periphery  of 
the  anterior  chamber  is  accounted  for  by  the  flattening  of  the  edge 
of  the  lens  during  accommodation.  There  is  often  no  change  in  the 
position  of  the  catoptric  images  as  described,  but  only  a  diminution 
in  the  size  of  the  image  formed  by  the  anterior  surface  of  the  lens, 
showing  that  the  surface  has  become  more  convex  but  has  not  ad- 
vanced to  any  appreciable  degree.  To  make  out  the  change  of  size 
in  the  lenticular  catoptric  image  during  accommodation  a  small  white 
and  well-illuminated  square  should  be  used  instead  of  the  candle 
flame,  as  the  object.     The  tension  of  the  anterior  chamber  of  the 


ACCOMMODATION.  lOI 

eyeball  diminishes  during  accommodation,  as  shown  by  Forster  in 
1864.  He  observed  in  patients  with  small  keratoceles,  that  the  pro- 
trusion diminished  in  size  during  accommodation,  to  swell  up  again 
as  the  accommodation  was  relaxed.  The  iris  covers  the  periphery  of 
the  lens,  so  whichever  theory  is  the  correct  one,  the  resulting  increase 
of  refraction  in  the  pupillary  area  is  the  same. 

In  support  of  the  Tscherning  theory  of  accommodation  is  cited  the 
fact  that  the  amplitude  of  accommodation  diminishes  towards  the 
edge  of  the  pupil,  as  detected  by  the  aberroscope.  This  instrument 
consists  of  a  strong  plano-convex  lens,  which  on  its  plane  side  carries 
a  micrometer  in  the  form  of  little  squares.  We  look  at  a  distant 
luminous  point  through  the  lens,  moving  it  to  10  to  20  cm.  from  the 
eye.  The  lens  causes  the  light  to  assume  the  shape  of  a  circle  of 
light,  and  upon  this  diffusion  circle  most  people  see  the  lines  in  the 
field  concave  towards  the  periphery,  due  to  the  usual  variety  of 
spherical  aberration  of  the  crystalline  lens,  namely  positive  aberration. 

But,  on  making  an  effort  at  accommodating,  the  forms  of  the 
shadows  change ;  they  now  turn  their  concavity  towards  the  center, 
indicating  that  the  refraction  increases  towards  the  center  of  the  lens, 
or  that  the  edge  of  the  lens  is  now  weaker  than  the  center ;  the  aber- 
ration has  been  overcome  by  accommodation. 

When  an  eye  looks  directly  at  an  object  the  macula  lutea  of  the 
retina  is  employed,  and  the  eye  is  said  to  have  fixed  the  object. 
This  is  central  or  direct  vision,  in  contradistinction  to  vision  performed 
with  the  peripheral  portions  of  the  retina,  namely,  indirect  vision. 
When  the  eyes  are  viewing  an  object  beyond  twenty  feet  from  them 
the  visual  axes  are  practically  parallel.  The  visual  axis  is  a  line 
drawn  from  the  macula  lutea  through  the  nodal  point  forward. 
When  a  near  object  is  fixed  the  visual  axes  must  deviate  inwards, 
towards  the  nose,  in  order  that  each  eye  may  receive  its  stimulus  on 
its  macula.  This  act  is  called  convergence,  and  the  angle  through 
which  the  visual  axis  of  each  eye  deviates,  in  fixing  a  near  object,  is 
the  angle  of  convergence.  The  unit  of  measurement  of  conver- 
gence is  the  meter-angle  (Nagle),  that  is  the  amount  of  convergence 


I02 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


that  is  necessary  to  fix  an  object  at  one  meter's  distance,  in   the 
median  Hne.     The  value  of  one  meter-angle  is  i  °  50'  for  each  eye, 

or  twice  that  amount  (3°  40')  for  one 
eye  if  the  object  of  fixation  is  directly 
in  front  of  one  eye. 

The  following  is  the  manner  of  de- 
duction if  the  object  is  in  the  median 
line  : 

00'  is  the  interocular  distance ; 
OM,  one  half  of  the  interocular  dis- 
tance ;  O M  is  perpendicular  to  00\ 
so  that  for  an  object  on  it  the  conver- 
gence of  each  eye  is  equal.  When  the 
visual  axes  JO  and  J'  O'  are  parallel 
the  convergence  is  nil ;  when  however  the  visual  line  has  deviated 
to   C',JO  has  moved  to  OCr.JOC' =  2ing\&  of  convergence. 

JO  being  parallel  to  CM,  angle /(9 C'  =  angle  OC'M.  In  rt.  A 
OC'M,  OMIOC'  =  s\nQZ.  OC'M.  The  value  of  (9 C J/ depends 
upon  the  interocular  distance.  The  average  interocular  distance  is 
64  mm.,  making  0M=  32  mm.  OC  =  1,000  mm.  (i  m.);  OM/  OC' 
=  32/1,000  =  .032  =  the  sine  of  one  meter-angle,  whiclj  corresponds 
to  an  angle  of  i  °  50'. 

The  amount  of  convergence  for  any  distance  is  ascertained  in  de- 
grees by  multiplying  the  number  of  meter  angles,  necessary  for  that 
distance  by  1°  50'.  The  number  of  meter-angles  of  convergence 
needed  for  a  given  distance  is  the  inverse  of  the  distance,  thus  :  for  2 
m.  there  is  needed  one  half  meter-angle  of  convergence  and  for  ^/^  m., 
2  meter-angles  of  convergence.  The  average  convergent  near-point 
denoted  as  c.  p.  =  2-3  in.  or  5-8  cm.,  giving  the  normal  limit  of  con- 
vergence equal  to  20-12.5  m.A  (meter-angles). 

The  meter-angle  is  closely  related  to  the  centrad  (v),  and  is  used 
to  numerate  prisms.  The  value  of  one  meter-angle  is  easily  ascer- 
tained by  finding  its  relation  to  a  centrad.  The  centrad  is  a  prims 
that  deviates  a  ray  i  / 100  part  of  a  radian,  that  is  an  arc  whose  length 


ACCOMMODATION. 


103 


is  equal  to  its  radius  of  curvature.  It  is  then  measured  upon  the 
tangent.  The  deviation  of  the  meter-angle  is  measured  on  the  sine 
(half  the  interocular  distance).  One  meter-angle  equals  a  deviation 
of  32  mm.  as  32  mm.  is  half  of  the  average  interocular  distance.  For 
small  angles  the  sine  and  the  arc  are  almost  equal.  At  one  meter's 
distance  the  amount  of  deviation  is  equal  to  3.2  centrads  (32  in  1,000 
or  3.2  in  100,  or  3.2  v)-  The  nearer  the  fixation  point;  the  greater 
the  convergence  necessary  to  maintain  single  binocular  vision  (seeing 
singly  with  the  two  eyes). 

The  accommodation  and  convergence  are  expressed  in  terms  that 
indicate  the  same  number  of  units  for  any  given  distance.     Thus  : 

an  E.  eye  viewing  an  object  at  33  cm.  needs  3  D.  Ace.  (  ^ — =---^ ) 

V  3  U-  Acc.y 
and  as  33  cm.  is  one  third  of  a  meter,  the  convergence  necessary  is 
3  m.Z».  While  using  5  D.  Accommodation,  5  meter-angles  of  con- 
vergence are  needed  by  the  emmetrope,  and  so  on. 

The  number  of  meter-angles  that  the  eyes  can  call  into  use  is  the 
measure  of  the  amount  of  convergence,  the  amplitude  of  convergence. 
It  is  measured  from  the  far-point  of  convergence  (C.  R.)  to  the  near 
point  of  convergence  (c.  p.).  C.  R.  is  the  point  for  which  the  visual 
lines  are  directed  when  the  convergence  is  relaxed  to  the  utmost ;  c.  p. 
the  point  for  which  the  visual  axes  are  directed  when  the  convergence 
is  at  its  utmost.  The  visual  lines  should  be  parallel  when  the  eyes  are 
adjusted  for  C.  R.  At  times  the  visual  lines  actually  diverge,  causing 
an  outward  cast,  and  at  other  times  there  is  convergence  constituting 
an  inward  cast  when  the  eyes  are  adjusted  for  C.  R.  Accommodation 
and  convergence,  as  has  been  shown,  are  very  closely  associated,  so 
that  for  every  diopter  of  accommodation  there  is  a  corresponding 
meter-angle  of  convergence.  The  methods  of  measuring  conver- 
gence will  be  described  under  the  head  of  muscular  inefficiencies. 

This  association  is  more  or  less  a  flexible  one,  however,  so  that 
accommodation  and  convergence  are  in  a  certain  measure  independ- 
ent of  each  other.  This  varies  in  different  individuals.  The  amount 
of  accommodation  that  can  be  exercised  without  altering  the  amount 


I04 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


of  convergence  is  called  the  relative  accommodation,  and  the  amount 
of  convergence  that  can  be  brought  into  use  without  altering  the 
amount  of  accommodation  is  the  relative  convergence.  A  patient  is 
made  to  fix  fine  print  at  33  cm.  distance.  Three  diopters  of  accom- 
modation are  in  use.  Suppose  that  p  lies  at  10  cm,;  there  is  then 
7  D.  of  absolute  accommodation  in  reserve  (100/10=  10,  10  —  3  = 
7  D.).  The  part  of  the  relative  accommodation  in  use  when  con- 
verging for  a  given  distance  is  the  negative  portion.  It  is  measured 
by  the  strongest  convex  spherical  lens  with  which  the  patient  can  see 
as  well  as  without  at  the  given  distance,  the  point  for  which  the  eyes 
are  converged.  As  the  spheres  are  added  the  accommodation  is  re- 
laxed pari  passu.  The  part  of  the  relative 
accommodation  in  reserve  is  the  positive 
portion.  It  is  revealed  by  the  strongest 
concave  spherical  lens  with  which  the  pa- 
tient can  see  as  well  as  without,  at  the  dis- 
tance for  which  the  eyes  are  converged. 
As  negative  spheres  are  added  the  accom- 
modation is  increased  pari  passu  until  the 
whole  amount  is  in  use.  The  far-point  of 
relative  accommodation  is  denoted  by  R^, 
and  the  near-point  by/i.  '- 

In  the  figure,  F.p.  is  the  fixation  point  at 
33  cm.  distance.     While  the  eyes  continue 
to  converge  for  the  point  P.p.,  they  can  ac- 
commodate for  a  more  distant  point  R^,  or  the  nearer  point  p^. 
If  ^1  is  I  m.  distant  and  /j,  20  cm.  distant,  then  : 

y^j  =^1  —  i?i  =  5  D.  —  I  D.  =  4  D.  relative  accommodation. 

The  print  held  at  F.p.  could  then  be  read  as  well  with  a  +  2  D.S.  as 
with  no  glass  before  the  eye ;  it  could  also  be  read  as  clearly  with 
a  —  2  D.S.  (100/33  cm.  —  3D.  accommodation,  100/20  =  5  D.  accom- 
modation, 5  —  3  D.  accommodation  =  2  D.).  With  a  minus  lens 
because  a  concave  lens  stimulates  accommodation. 


ACCOMMODATION.  •  105 

The  relative  accommodation  varies  for  each  point  of  fixation.  The 
amount  of  positive  relative  accommodation  decreases  as  the  fixation 
point  approaches  the  eyes.  Upon  the  relation  of  the  segments  of 
relative  accommodation  to  each  other  depends  the  ability  of  the  eyes 
to  work  without  exhaustion,  keeping  up  the  necessary  amount  of 
accommodation  and  convergence.  It  is  impossible  to  use  the  eyes 
for  a  distance  at  which  the  positive  portion  of  the  relative  accommo- 
dation is  not  at  least  as  great  as  the  negative  portion,  otherwise 
fatigue  soon  results.  At  the  distance  of  33  cm.,  the  proper  reading 
distance,  the  plus  portion  of  the  relative  accommodation  is  about  one 
and  one  half  times  greater  than  the  minus  portion,  for  which  reason 
work  can  be  carried  on  at  this  distance  continuously  without  tiring. 
A  lack  of  unity  of  accommodation  and  convergence  is  seen  in  the 
eye  at  the  near  point.  The  function  of  convergence  being  stronger 
than  that  of  accommodation,  the  absolute  near  point  is  obtained  at 
the  sacrifice  of  single  binocular  vision,  the  convergence  overacting 
and  thus  reinforcing  the  accommodation. 

In  hyperopia  the  amount  of  accommodation  required  is  greater 
than  in  emmetropia,  and  the  same  tendency  for  the  two  functions  to 
reinforce  each  other  offers  a  stimulus  to  convergence  which  often 
results  in  internal  squint. 

Optical  Defects. — The  crystalline  lens  of  the  eye,  as  has  been 
pointed  out  in  a  former  chapter,  possesses  the  errors  of  spherical  and 
chromatic  aberration,  both  of  which  defects  interfere  with  the  distinct- 
ness of  the  retinal  images.  In  order  that  two  objects  side  by  side 
can  be  recognized  as  two,  they  must  be  separated  at  least  by  60",  so 
that  the  images  of  both  do  not  fall  upon  the  same  retinal  percipient 
element,  as  under  these  conditions  two  objects  are  not  seen,  but  only 
one,  the  brain  interpreting  the  stimulation  of  the  same  element  twice, 
as  one  stimulation,  from  one  object  in  space.  If  the  retina  was  per- 
fect two  objects  should  be  perceived  even  if  their  images  did  fall 
upon  the  same  end  element  of  the  optic  nerve.  The  dioptric  system 
of  the  eyeball,  furthermore,  is  a  decentered  system,  that  is,  the  center 
of  the  cornea  is  not  in  line  with  the  center  of  the  lens,  nor  the  center 


I06  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

of  the  lens  in  line  with  the  macula  lutea.  A  line  drawn  from  the 
center  of  the  retina  forward  through  the  center  of  the  lens  is  called 
the  optic  axis.     This  line  does  not  cut  the  central  point  of  the  cornea. 

A  line  from  the  point  of  fixation  to  the  macula  is  called  the  visual 
axis ;  it  cuts  the  optic  axis  at  the  nodal  point,  forming  with  it  an  angle 
called  the  angle  beta.*  The  optic  axis  outside  of  the  eyeball  runs 
below  and  to  the  outer  side  of  the  visual  axis,  while  within  the  eye- 
ball it  runs  to  the  inner  side  of  and  above  the  visual  axis.  The 
visual  axis  as  a  rule  pierces  the  cornea  a  little  to  its  nasal  side. 

The  corneal  curve  continued  (that  of  anterior  surface)  forms  an 
ellipse,  the  major  axis  of  which,  that  is  the  corneal  axis,  runs  to  the 
outside  of  the  visual  axis  and  forms  with  it  the  angle  called  angle 
alpha.  The  angle  alpha  is  usually  equal  to  about  five  degrees,  and 
is  considered  positive  when  the  visual  line  lies  to  its  inner  side,  and 


Object 


I  Macula. 
/Center  of  Retina 


C  —Center  of  Lens 
C  -=  Center  of  Rotation 
N  -  Nodal  Point 


negative  when  to  its  outer  side.  In  E.  and  H.  it  is  the  rule  to  have 
the  angle  with  a  positive  value,  and  when  large  it  often  causes  the 
eye  to  have  an  apparent  ontward  cast.  In  M.  it  is  negative  and  then 
causes,  if  large,  an  apparent  inward  cast. 

The  line  of  fixation  is  drawn  from  the  object  for  which  the  eye  is 
directed  to  the  point  of  rotation,  a  point  in  the  vitreous  chamber  6 
mm.  behind  the  nodal  point  and  9  mm.  in  front  of  the  retina.  About 
this  point  the  eyeball  makes  all  of  its  movements  as  if  upon  a  pivot. 
The  angle  formed  by  the  fault  of  the  optic  axis  and  the  line  of  fixa- 
tion is  the  angle  gamma,  and  the  angle  between  the  corneal  axis  and 
the  Hne  of  fixation  has  been  called  the  angle  kappa  (see  figure). 

*  Often  called  angle  alpha. 


CHAPTER  VII 

OPHTHALMOSCOPY    AND    OBLIQUE    ILLUMINATION 

All  objects  that  do  not  shine  by  their  own  light  are  visible  to  us 
by  the  light  that  is  thrown  off  from  them  by  reflection  entering  our 
eyes.  The  interior  of  the  eyeball  is  illumined  but  the  pupil  ap- 
pears black  under  ordinary  conditions,  as  the  light  that  is  re- 
flected back  from  the  interior  of  the  eye  does  not  enter  the  eye  of 
the  observer. 

The  blackness  of  the  pupil  was  formerly  supposed  to  be  due  to 
the  absorption  of  the  light  that  entered  the  eye  by  the  black  pigment 
that  coats  the  interior  of  the  eyeball.  In  1850  Briicke  and  Gum- 
ming discovered  the  means  of  making  the  pupil  of  the  human  eye 
luminous,  and  in  the  year  1851  Helmholtz  invented  the  ophthalmo- 
scope, the  instrument  that  has  revolutionized  ophthalmology.  Light 
passes  out  of  an  observed  eye  along  paths  close  to  those  of  entrance. 
The  ophthalmoscope  allows  the  observer  to  get  his  eye  in  a  position 
relative  to  the  observed  eye,  to  receive  some  of  the  returned  light 
from  the  latter,  and  as  the  observer's  eye  placed  back  of  the  sight- 
hole  in  the  mirror  of  the  ophthalmoscope  is  practically  at  the  source 
of  light  to  the  observed  eye,  the  pupil  of  the  latter  appears  illumined. 
Helmholtz  first  was  able  to  see  the  interior  of  the  eyeball  by  reflect- 
ing light  into  it  from  a  plate  of  glass  held  obliquely  before  his  own 
eye.  The  reflecting  power  of  the  glass  was  increased  by  placing 
several  plates  together.  Plane  amalgamated  mirrors  were  soon  used 
as  reflectors,  and  finally  after  the  suggestion  of  Reute,  concave 
mirrors  came  into  use  for  ophthalmoscopic  mirrors.  The  concave 
mirror  gives  better  illumination,  as  it  gathers  up  or  focuses  the  light 
that  enters  the  eye.  The  ophthalmoscope  is  still  to-day  nothing  but 
a  reflector  with  a  central  peep-hole. 

107 


io8 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


Observed 


Observer 


In  the  figure  the  light  enters  the  eye,  E,  along  the  dotted  lines,  ss\ 
illuminating  the  area  ab  upon  the  retina.  The  light  reflected  back 
passes  out  of  the  eye  along  paths  embraced  by  the  lines  rr\  drawn 
through  the  nodal  point  N.  The  observer's  eye  E'  receives  no  light 
firom  the  eye  E,  so  the  pupil  of  E  remains  unillumined  to  E' .    Rays  s 

and  r',  and  s'  and  r, 
from  points  a  and  b  re- 
spectively pass  out  of  the 
o  eye  parallel  as  the  retina 
h  of  the  eye  lies  at  the 
principal  focus  of  its  diop- 
tric system,  as  the  eye  is 
emmetropic.  If  the  ob- 
server would  move  close 
enough  to  receive  some 
returned  rays  from  the 
observed  eye,  his  head  would  then  intercept  the  entrance  of  light 
into  the  observed  eye. 

In  the  hyperopic  eye  one  is  able  to  see  the  pupil  illuminated,  espe- 
cially if  it  is  dilated.  The  reason  is  that  the  light  passes  out  of  the 
hyperopic  eye  in  diverging  paths  and  some  falls  into  the  eye  of  the 
observer  near  by. 

If  in  the  preceding  figure  the  retina  was  moved  to  the  position  of 
H,  the  eyeball  would  be  hyperopic.  The  light  returning  from  the 
area  of  illumination  {a'b'^  would  be  embraced  by  the  rays  r"  and  s", 
and  as  the  observer's  eye  receives  some  of  this  returned  light,  the 
pupil  of  the  observed  eye  would  appear  aglow.  Rays  of  light  from 
the  same  point  in  the  fundus  of  the  hyperopic  eye  leave  the  eyeball 
diverging  as  rays  ss"  from  the  point  a\  and  s'r"  from  the  point  b\ 
because  the  retina  of  the  hyperopic  eye  lies  anterior  to  the  principal 
focus  of  the  dioptric  system  of  the  eyeball.  The  eyes  of  many  ani- 
mals are  hyperopic,  the  reason  in  part  that  such  eyes  are  seen  aglow. 
The  luminosity  of  their  pupils  is  however  enhanced  by  a  peculiar  re- 
flecting medium  in  the  chorioid  coat  of  their  eyes,  called  the  tapetum. 


OPHTHALMOSCOPY   AND   OBLIQUE   ILLUMINATION. 


109 


(Some  observers  claim  that  the  eyes  of  beasts  and  birds  are  naturally 
emmetropic  and  not  hyperopic.)  Human  eyes  that  are  devoid  of 
lenses  are  intensely  hyperopic  and  their  pupils  are  therefore  luminous. 
This  is  seen  after  cataract  extraction,  especially  if  an  iridectomy  has 
been  done.  The  luminosity  of  the  pupils  of  the  albino's  eyes  is  ex- 
plained in  a  different  way.  The  light  passes  into  the  albino's  eyes  not 
only  through  the  pupils  but  also  through  the  non-pigmented  iris,  and 
even  through  the  thin  sclerotics  which  are  peculiar  to  such  eyes.  Not 
only  a  limited  area  of  fundus  is  illuminated  at  one  time  as  in  other 
eyes,  but  the  whole  fundus  is  flooded  with^light ;  the  rays  of  light  from 
different  parts  of  the  fundus  pass  out  of  the  pupil  and  pass  in  all  direc- 
tions in  space,  some  of  which  enter  the  eye  of  the  observer  near  by. 
That  this  is  the  correct  explanation  is  proven  by  the  fact  that  the 
pupil  of  the  albino's  eye  looks  black  as  soon  as  a  screen  with  a  hole 
in  it  the  size  of  the  normal  pupil  is  placed  before  the  eye.  This  ex- 
cludes all  light  from  the  eyeball  save 
that  which  enters  through  the  pupil, 
making  the  eye  of  the  albino  like  that^ 
of  a  normal  person  in  this  respect. 

Light  from  the  original  source  of 
light  at  L  is  reflected  by  the  mirror 
M  (immediate  source)  into  the  ob- 
served eye,  along  the  paths  marked 
by  the  dotted  lines.  The  returning 
rays  pass  out  of  the  observed  eye 
along  the  paths  marked  by  continuous  lines  through  the  sight-hole 
of  the  ophthalmoscopic  mirror  into  the  eye  of  the  observer.  The 
observer  is  therefore  enabled  to  see  the  interior  of  the  observed 
eyeball.  There  are  many  kinds  of  ophthalmoscopes  on  the  market. 
The  simple  ophthalmoscope  is  a  mirror  with  a  central  opening  or  an 
area  where  the  amalgam  is  wanting.  Some  have  round  mirrors,  others 
oblong  tilting  mirrors.  The  round  mirrors  are  preferable  as  the  area 
of  illumination  produced  by  them  is  circular,  while  that  from  an  oblong 
mirror  is  more  or  less  drawn  out  into  a  streak,  curtailing  somewhat 


Observer 


no  THE   EYE.    ITS    REFRACTION   AND    DISEASES. 

one's  view  of  the  fundus  (the  area  of  illumination  from  a  circular  con- 
cave mirror  is  a  circle  if  the  mirror  is  out  of  focus,  and  especially  if 
the  source  of  light  is  at  some  distance  from  the  mirror).  Refraction 
ophthalmoscopes  have  in  addition  a  number  of  lenses  that  can  be  re- 
volved behind  the  sight-hole  of  the  mirror  and  before  the  eye  of  the 
observer,  so  that  the  light  returning  from  the  observed  eye  can  be 
given  the  direction  necessary  to  bring  it  to  an  accurate  focus  upon  the 
retina  of  the  observer.  The  best  refraction  ophthalmoscope  is  the 
one  with  the  largest  number  of  lenses  and  the  one  in  which  any  com- 
bination or  strength  of  lens  can  be  gotten  with  the  least  possible  com- 
plication. Morton's  ophthalmoscope  is  probably  the  best  on  the  mar- 
ket, as  the  lenses  are  contained  in  an  endless  chain  that  revolves 
before  the  sight-hole  of  the  mirror.  The  use  of  the  refraction  oph- 
thalmoscope will  be  explained  under  the  head  of  errors  of  refraction. 
The  Loring  ophthalmoscope  is  probably  the  most  widely  employed 
and  is  an  excellent  instrument,  except  for  the  correction  of  refraction 
errors.  The  following  cuts  show  a  few  of  the  many  varieties  of  oph- 
thalmoscopes. The  Meyrowitz  model  of  the  Morton  ophthalmoscope 
is  in  all  respects  as  good  as  the  imported  original  model  of  Curry  and 
Paxton,  London. 

The  red  glare  that  fills  the  pupil  of  the  eye  when  viewed  with  the 
ophthalmoscope  is  called  the  chorioidal  reflex.  It  is  the  reflection 
back  from  the  vascular  chorioidal  coat  of  the  eye.  With  the  ophthal- 
moscope the  interior  of  the  eyeball  can  be  studied  in  detail.  Many 
diseases  on  the  interior  of  the  eye  that  formerly  lay  hidden  from  view 
now  lie  exposed  as  upon  the  surface.  In  the  interior  of  the  eyeball 
nerves  and  blood-vessels  can  be  studied  which  are  nowhere  else  in 
the  body  exposed  to  view  except  by  dissection.  The  eye-ground  is 
frequently  an  index  to  troubles  located  in  distant  organs  of  the  body, 
as  in  the  kidney  per  example,  and  in  many  grave  conditions  the  use 
of  the  ophthalmoscope  gives  the  most  important  diagnostic  signs. 
There  are  two  methods  employed  to  see  the  interior  of  the  eye, 
namely,  the  direct  and  indirect  methods  of  ophthalmoscopy.  The 
indirect  method  is  the  more  easily  mastered,  and  as  a  whole  more 


OPHTHALMOSCOPY   AND   OBLIQUE   ILLUMINATION. 


1 1  I 


1.  Loring's  Ophthalmoscope,  with  7  lenses,  set  in  revolving  disc,  with  round  or  tilting  mirror. 

2.  Loring's  Complete  Ophthalmoscope,  with  3  rows  of  figures,  tilting  mirror  and  covered  disc. 
This  instrument  consists  of  a  full  disc  and  a  quadrant  of  a  disc,  as  shown  in  the  cut.     The  quadrant 

rotates  immediately  over  the  disc  and  around  the  same  center,  and  contains  4  lenses,  — .50 — 16  and 
I  CO  +  16.  When  not  in  use  the  quadrant  is  beneath  its  cover,  and  the  instrument  then  represents  a 
simple  ophthalmoscope  with  16  lenses,  the  series  running  with  an  interval  of  i  D.,  and  extending  from 
I  to  7  plus  and  from  i  to  8  minus.  If  the  higher  numbers  are  desired  they  are  obtained  by  combina- 
tion with  those  of  the  quadrant.  These  progress  regularly  up  to  16  D.,  every  dioptric  being  marked 
upon  the  disc ;  above  this  up  to  -f  23  D.  and  —24  D.  we  simply  have  to  add  the  glass  which  comes 
beneath  the  16  D.,  turning  always  in  the  same  direction. 


112 


THE    EYE,    ITS    REFRACTION    AND    DISEASES. 


useful,  except  in  the  estimation  of  refraction  errors  and  in  studying 
small  details  of  the  fundus.  By  the  indirect  method  more  of  the  fun- 
dus is  seen  at  one  time,  although  not  as  much  enlarged  as  when  seen 
by  the  direct  method.  To  study  a  lesion  under  magnification,  then, 
the  direct  method  is  preferable. 

It  is  well  for  the  beginner  in  ophthalmoscopy  to  have  the  pupil  of 
the  eye  to  be  examined  expanded  by  a  mydriatic,  as  then  more  light 
can  enter  the  eye  and  consequently  the  picture  of  the  fundus  will  be 
seen  more  clearly,  and  furthermore,  the  reflection  of  the  light  from 


3  4 

3.  Loring's  Ophthalmoscope. 

4.  Loring's  Post-Graduate  Ophthalmoscope,  with  round  or  tilting  mirror. 

Consists  of  two  superimposed  dies,  by  means  of  which  31  combinations  can  be  made.  The  lower 
disc  contains  15  convex  lenses,  from  .50  to  17.50  D.,  giving  the  convex  series  ;  in  the  upper  disc,  which 
serves  also  as  a  cover,  is  a  concave  18  D.  lens,  which  when  brought  into  position  before  the  mirror  hole 
gives  a  series  of  16  concave  lenses  from  .50  to  18  D. 


OPHTHALMOSCOPY   AND    OBLIQUE   ILLUMINATION. 


113 


5  -   B 

(Full  size  cut  of  Dr.  Knauer's  Ophthalmoscope.) 
Fig.  a,  back  of  instrument,  showing  mirror  and  slide  on  front  in  dotted  lines. 
Fig.  B,  same,  with  cover  removed,  showing  interior  mechanism. 


5.   Knauer's  Ophthalmoscope. 

The  Knauer  Ophthalmoscopa  is  an  instrument  of  novel  design  and  its  main  features  are  the  great 
range  of  foci,  its  compactness,  ease  of  manipulation  and  simplicity  of  construction.  It  contains  two  discs 
holding  lenses  of  different  foci,  so  arranged  that  whatever  focus  may  be  produced  by  their  combination, 
is  plainly  indicated  in  the  little  window  situated  in  the  center  of  the  back  of  the  Ophthalmoscope,  where 
both  the  number  and  the  sign  of  the  lenses  in  si.u  appear. 

A  special  point  in  the  construction  of  the  instrument  is  that  all  the  gear-work  is  completely  covered. 

The  lower  disc  is  operated  by  the  small  driving  wheel,  and  this  disc  again  acts  automatically  upon 
the  upper  disc  in  such  a  manner  that  the  consecutive  combinations  are  effected  in  intervals  of  one  diopter 
from  -)-  I  D.  to  -f-  20  D. ,  and  from  —  I  D.  to  —  39  D.  There  is  besides,  situated  behind  the  tilting 
mirror,  a  slide  containing  a  -|-  -5  D.  lens,  which  can  be  brought  in  instant  combination  with  any  of  the 
lenses  in  the  series  by  an  easy  and  natural  movement  of  the  index  finger,  thus  giving  a  regular  interval 
oi  .5  D.  from  -f  .5  to  -\-  20.5  D.,  and  from  — .5  D.  to  — 39  D.,  making  in  all  119  combinations. 

8 


114 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


For  tie  purpose  of  rapidly  changing  the  lenses,  the  upper  disc  can  be  revolved  indepenc.ently  by 
means  ci"  two  small  projecting  pins,  a  slight  turn  of  the  same  causing  a  change  of  lO  numbers  in  the 
series;  if,  for  instance,  the  — 38  D.  were  before  the  opening,  a  simple  turn  of  the  upper  disc  would 
change  it  rapidly  to  — 28  D.,  — 18  D.,  or  — 8  D.,  thus  obviating  the  turning  of  the  small  driving 
wheel  until  the  lower  focus  is  reached  in  single  numbers. 

The  small  driving  wheel  that  operates  the  discs  is  so  placed  that  the  finger  of  the  operator  is  not 
brought  between  the.  Ophthalmoscope  and  the  face  of  the  patient. 

6.   Payne's  Ophthalmoscope,  with  tilting  mirror. 

Consists  of  two  superimp)osed  discs,  each  holding  respectively  17  convex  and  concave  lenses,  ranging 
from  0.25  D.  to  20  D.  The  rotation  of  the  discs  is  accomplished  by  means  of  two  small  cogged  driv- 
ing wheels. 


Roth's  improved  Ophthalmoscope  with  automatic  quadrant  and  index  and  tilting  mirror. 

In  the  construction  of  this  Ophthalmoscope  the  general  plan  and  dimensions  recommended  by  Loring 
have  been  adhered  to,  and  the  object  of  the  improvement  is  mainly  to  overcome  the  difficulty  experienced 
in  obtaining  and  reading  the  higher  combinations,  which  formerly  necessitated  the  removal  of  the  instru- 
ment from  the  eye  to  bring  the  quadrant  lenses  before  the  sight  hole,  thus  interrupting  the  examination. 
Dr.   Roth  has  completely  overcome  this  difficulty  by  his  invention  of  the  Automatic  Quadrant  and 


OPHTHALMOSCOPY  AND   OBLIQUE   ILLUMINATION. 


115 


Registering  Index,  which  greatly  S'mphfies  the  manipulation  of  the  instrument,  inasmuch  as  the  com- 
bination of  the  higher  numbers  is  effected  automatically  by  a  continuous  revolution  of  the  disc,  which 
also  moves  a  pointer  which  indicates  the  number  of  each  lens  or  combination  of  lenses  plainly  upon  a 
dial 

In  addition  to  the  lenses  contained  in  the  disc  and  quadrant,  a  +  .50  D.  lens  is  mounted  in  a  slide 
attached  to  the  front  of  the  instrument,  directly  behind  the  tilting  mirror,  in  such  a  manner  that  it  can 
instantly  be  brought  into  combination  with  any  of  the  lenses  contained  in  the  series  by  an  easy  and 


natural  movement  of  the  index  finger,  thus  giving  a  regular  interval  of  .50  D.  throughout  the  entire 
series  from  +  .50  D.  to  +23.50  D.,  and  from  —.50  D.  to  —24  D.,  making  in  all  95  distinct  com- 
binations. 

Fig.  7  shows  the  exact  size  of  the  Ophthalmoscope  with  the  index  finger  pointing  to  o.  The  convex 
series,  which  are  shown  in  white  figures  on  the  instrument,  occupy  the  inner  circle,  while  the  concave 
numbers,  which  are  marked  in  red,  run  in  the  reverse  direction  toward  the  outer  margin  of  the  dial. 


Il6  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

Fig.  8.     Same  with  small  driving  wheel. 

Morton's  ophthalmoscope  consists  essentially  of  twenty- nine  separate  lenses,  inclosed  in  an  endless 
groove  and  propelled  by  a  strong  driving  wheel.  In  addition  to  the  lenses  just  mentioned  are  four 
others,  set  in  a  separate  disc,  and  so  placed  that  they  can  be  instantly  put  in  front  of  or  removed  away 
from  the  sight  hole  without  rotating  the  whole  series  of  convex  or  concave  lenses.  At  the  same  time 
that  the  driving  wheel  propels  the  lenses  it  rotates  a  disc  on  which  at  a  certain  aperture  is  indicated  the 
lens  presented  at  the  sight  hole. 

On  the  front  of  the  instrument  is  an  arrangement  similar  to  the  nosepiece  of  a  microscope,  revolving 
on  a  central  pivot  and  carrying  three  mirrors  —  one  plane  and  one  concave  mirror  of  lo-inch  focus  at 
one  end  and  a  small  concave  mirror  of  3-inch  focus  at  the  other.  The  first  two,  which  are  set  back  to 
back  in  one  mounting  and  are  reversible,  are  for  indirect  examination  and  retinoscopy. 

The  advantages  claimed  for  this  Ophthalmoscope  are,  briefly : 

1 .  A  continuous  series  of  single  lenses,  sufficient  for  all  ordinary  purposes. 

2.  The  provision  of  a  few  separate,  easily  adjustable,  lenses  for  extraordinary  cases. 

3.  The  lens  in  the  sight  hole  is  always  shown  on  the  indicating  disc  ( except  in  the  rare  cases  where 
one  of  the  extra  lenses  just  mentioned  is  used). 

4.  The  numbers  of  the  lenses  and  their  relative  jxjsitions  being  fully  exjxjsed  on  an  indicating  disc, 
the  direction  in  which  this  latter  has  to  be  rotated  to  bring  any  particular  lens  to  the  sight  hole  is  at 
once  made  manifest. 

5.  There  is  only  one  driving  wheel. 

6.  A  pupilmeter,  which  is  set  in  the  face  of  the  driving  wheel. 

7.  The  provision  of  two  mirrors  revolving  on  a  central  pivot,  "so  that  either  can  be  at  once  brought 
into  position. 

8.  The  width  of  the  instrument  is  only  I  ^  inches,  while  the  driving  wheel,  being  3  inches  below 
the  sight  hole,  is  unimpeded  in  its  action  by  contact  with  the  face  of  observer  or  patient. 

9.  Lastly,  the  instnmient  balances  well  in  the  hand,  is  light  and  packs  into  a  small  compass. 

the  cornea  of  the  observed  eye  is  not  so  annoying.  The  room  should 
be  dark  and  the  source  of  Hght  shaded.  The  latter  is  not  neces- 
sary, however,  but  if  the  source  of  light  is  a  circular  opening  in  an 
opaque  shade  covering  the  flame,  the  beginner  is  not  so  much  con- 
fused by  the  image  of  the  flame  or  source  of  light  in  the  eye  to  be 
observed. 

If  the  source  of  light  is  not  shaded  it  is  well  to  have  it  at  some  dis- 
tance from  the  mirror,  as  then  the  area  of  illumination  from  the  con- 
cave mirror  is  much  out  of  focus  and  hence  more  circular  in  outline. 
The  most  convenient  source  of  light  is  an  Argand  gas-burner.  The 
Welsbach  light  is  too  bright  and  very  trying  upon  the  eyes  of  the 
patient ;  it  is  also  not  easy  to  estimate  a  slight  change  in  the  color  of 
the  fundus  of  the  eye,  as  in  incipient  inflammatory  changes,  when  the 


OPHTHALMOSCOPY   AND   OBLIQUE   ILLUMINATION. 


117 


source  of  light  is  so  powerful.  Indeed,  one  often  lessens  the  illumi- 
nation of  the  eye  by  using  a  plane  mirror  when  searching  for  small 
lesions. 

The  Indirect  Method.  —  The  patient  and  the  examiner  sit  opposite 
one  another  and  about  arm's  length  from  each  other.  Their  eyes 
should  be  at  about  the  same  height,  and  the  source  of  light  back  of  the 
patient  and  upon  his  left  hand.  Holding  the  handle  of  the  ophthal- 
moscope horizontally,  and  with  the  edge  of  the  mirror  against  the 
side  of  the  nose  the  examiner  reflects  the  light  into  the  eye  to  be 
examined.  The  pupil  is  seen  at  once  to  become  luminous,  but  no  de- 
tails of  the  interior  of  the  eyie  are  seen  unless  there  be  present  an 
error  of  refraction,  either  myopia  or  hyperopia,  in  the  observed  eye. 
Holding  the  reflection  steady  in  the  eye,  a  convex  spherical  lens  of 
about  2  to  3  (20  D.  to  13  D.)  inch  focal  distance  is  held  before  the 
eye  at  about  its  focal  length.     This  lens  is  spoken  of  as  the  objective 


Original  Source  of  Light 

A 


Observer's  Eye 


Observed  Eye 


(The  relative  Sizes  of  1,  a,and  a'  are  not  Accurate) 


lens.  It  should  be  held  between  the  thumb  and  index  finger  of  the 
left  hand  and  the  hand  steadied  by  resting  the  little  finger  against 
the  brow  or  forehead  of  the  patient.  No  attempt  should  be  made  to 
look  through  the  objective  lens  into  the  eye,  as  nothing  will  be  seen; 
but  the  attention  should  be  directed  to  a  point  just  in  front  of  the 
objective  lens,  that  is  in  the  air  between  yourself  and  the  patient,  as 
it  is  here  that  a  real  image  of  the  fundus  of  the  eye  is  formed.  See 
figure  on  preceding  page  for  explanation. 


Il8  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

The  continuous  lines  are  rays  of  illumination  to  the  eyeball  A ; 
dotted  lines,  the  returning  rays  of  light  from  the  eyeball  A,  forming 
the  image  a  of  the  fundus  /  through  the  objective  lens  L.  The 
broken  lines  represent  the  light  from  the  image  a  to  the  fundus  of 
eye  B  ;  a\  image  on  retina  of  eyeball  B  of  the  image  a.  The  image 
formed  by  the  indirect  method  of  ophthalmoscopy  is  inverted.  What- 
ever is  above  in  the  image  is  below  in  the  eyeball,  and  that  to  the 
right  in  the  image  is  upon  the  left  in  the  eyeball,  and  vice  versa. 
Accommodation  or  an  equivalent  convex  lens  is  needed  to  see  the 
image  of  the  fundus  of  an  eye  by  the  indirect  method.  The  image 
has  a  contrary  motion  also;  that  is,  if  the  observer  moves  upward, 
the  image  moves  downward  ;  if  the  observer  moves  to  the  right,  the 
image  moves  to  the  left  and  so  on.  The  upper  part  of  the  image 
must  be  viewed  if  it  is  desired  to  see  the  lower  part  of  the  eye-field, 
and  the  right  side  of  the  iftiage  if  the  portion  of  the  eye-field  to  the 
left  is  to  be  examined. 

Heine  describes  the  following  method  of  examining  one's  own  eye 
by  the  indirect  method.  An  ordinary  hand  mirror  is  held  between 
the  light  and  the  left  eye,  so  as  to  shade  it ;  then  with  an  ophthal- 
moscopic mirror  the  light  is  reflected  into  the  left  eye  by  aid  of  the 
hand  mirror,  illuminating  the  region  of  the  fundus  >to  the  temporal 
side  of  the  fovea.  Now,  by  holding  a  convex  lens  of  13  D.  before 
the  left  eye  the  inverted  image  of  the  fundus  is  seen.  By  converg- 
ing the  left  eye  strongly  the  entrance  of  the  optic  nerve  may  be  ex- 
amined in  the  inverted  image. 

Direct  Method  of  Ophthalmoscopy.  —  (Also  called  the  method  of 
the  upright  or  erect  image.)  By  this  method  the  observer  approaches 
quite  close  to  the  patient  and  looks  directly  into  the  eyeball  without  the 
interposition  of  any  lens.  To  examine  the  right  eye  of  the  patient 
the  observer  uses  his  right  eye,  and  vice  versa,  so  that  the  noses  will 
not  interfere  with  getting  as  close  as  is  necessary  to  the  patient's  eye. 
The  light  should  be  placed  behind  and  on  the  side  of  the  patient's 
head  next  to  the  eye  under  examination,  about  on  a  level  with  his 
ear,  so  that  it  will  illuminate  his  temple,  leaving  his  eye  and  his  face 


OPHTHALMOSCOPY    AND    OBLIQUE    ILLUMINATION.  II9 

in  darkness.  Holding  the  instrument  in  the  right  hand,  if  the  right 
eye  is  to  be  examined,  the  observer  throws  the  Hght  into  the  patient's 
eye  from  a  distance  of  several  inches.  He  then  approaches  closer, 
all  the  time  keeping  the  light  in  the  eye  until  the  ophthalmoscopic 
mirror  is  almost  in  contact  with  the  patient's  eye.  The  observer 
must  not  attempt  to  look  directly  into  the  eye,  as  with  the  use  of 
accommodation  nothing  of  the  interior  of  the  eyeball  will  be  seen, 
unless  the  observer's  or  the  observed  eye  is  hyperopic.  Any  refrac- 
tion error  of  the  observer  should  be  corrected  by  the  wearing  of 
proper  spectacles,  and  then  no  confusion  will  arise  from  its  presence. 
One  should  stare  vacantly  into  the  eyeball  as  if  trying  to  see  an  ob- 
ject at  some  distance  behind  the  patient's  head.  The  accommodation 
may  be  encouraged  to  relax  by  forcibly  elevating  the  upper  eyelids. 
The  effect  of  this  over  accommodation  may  be  seen  thus :  If,  while 
reading,  the  upper  lids  be  elevated  forcibly,  the  printed  matter  will 
fade  out  of  legibility.  The  patient  should  gaze  vacantly  into  space 
and  avoid  looking  into  the  light  as  reflected  from  the  mirror,  other- 
wise the  pupil  will  contract  to  its  utmost,  interfering  greatly  with  the 
test.  If  it  is  not  convenient  to  place  the  patient  under  the  effect  of 
a  mydriatic  it  is  a  good  plan  to  have  him  look  at  some  large  letters 
hung  at  a  distance  of  twenty  feet  across  the  room  which  is  made 
semi-dark,  so  as  to  encourage  the  accommodation  to  relax.  The 
examination  of  the  cornea  and  of  the  lens  of  the  eye  are  made  by 
placing  a  magnifying  lens  back  of  the  sight-hole  of  the  ophthalmo- 
scope. 

A  20  D.  S.  lens  is  a  convenient  strength  to  use.  In  order  to  make 
the  lens  magnify  a  lesion  of  the  cornea  it  is  necessary  to  view  the 
cornea  from  a  point  closer  than  the  focal  point  of  the  lens.  The 
focal  interval  of  a  20  D.  lens  is  5  cm.  (100-^20  =  5  cm.),  therefore 
the  examiner  must  draw  closer  than  5  cm.  to  the  eye  to  be  examined. 
Any  opacity  of  the  media  of  the  eyeball  looks  black  by  reflected  light, 
no  matter  what  its  color  may  be.  (At  times  the  opacity  is  dense 
enouo-h  to  be  seen  by  the  light  that  it  reflects,  and  then  it  is  seen  in 
its  true  color.     Hemorrhage  into  the  vitreous,  cataracts  and  dense 


I20  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

scars  of  the  cornea  are  often  seen  in  their  true  color  by  reflected  light.) 

Let  O  be  an  opacity  of  any 
sort  in  one  of  the  media  of  the 
eyeball.  As  no  light  can  enter 
the  eye  through  the  opacity,  rays 
a  and  b  being  excluded,  there 
can  be  no  returned  light  from  the 
eye,  and  the  pupil  in  that  locality,  in  consequence,  looks  black.  After 
examining  the  cornea  and  the  lens  with  the  20  D.  S.  lens  back  of  the 
sight-hole  of  the  ophthalmoscopic  mirror  the  motility  of  the  iris  should 
be  tested,  whether  it  reacts  evenly  and  promptly  under  the  influence 
of  light  thrown  into  the  eye  from  different  directions.  The  vitreous 
is  examined  by  throwing  light  into  the  eye  from  a  distance  of  eigh- 
teen to  twenty  inches  while  the  eyeball  is  moved  up,  down,  in  and 
out.  Opacities  in  the  vitreous,  neoplasms  and  a  detached  retina  are 
seen  in  the  erect  image,  because  they  are  within  the  range  of  accom- 
modation of  the  observer.  If  he  views  them  at  a  closer  distance  he 
must  place  a  convex  lens  behind  the  sight-hole  of  the  ophthalmo- 
scope, to  accommodate  or  converge  the  rays  of  light  for  him  as  they 
enter  his  eye ;  otherwise  nothing  but  an  indistinct  image  will  result. 
It  is  always  better  to  use  a  convex  spherical  lens  than  accommoda- 
tion in  ophthalmoscopic  examinations,  for  if  one  accommodates  at 
times  and  relaxes  accommodation  at  other  times  he  will  not  acquire 
as  good  a  control  over  his  ciliary  muscle  as  if  he  gets  into  the 
habit  always  of  viewing  the  interior  of  an  eye  with  relaxed  accom- 
modation. And,  unless  accommodation  is  completely  relaxed  one 
cannot  get  any  reliable  information  in  regard  to  the  refraction  error 
of  the  eye  under  examination.  To  place  or  locate  properly  an 
opacity  in  the  transparent  media  of  the  eye,  the  parallactic  test  is 
employed. 

If  the  opacity  is  a  faint  one  the  plane  mirror  is  used  to  the  best 
advantage.  It  is  necessary  at  times  to  ascertain  whether  the  opacity 
is  movable  or  fixed.  If  movable  it  will  be  seen  to  float  about  in  the 
eyeball  when  the  latter  is  moved  up,  down,  in  and  out,  while  the 


OPHTHALMOSCOPY   AND    OBLIQUE    ILLUMINATION.  121 

light  is  kept  steady  in  the  eye ;  the  observer  watching  the  pupil.  If 
the  opacity  is  immobile  its  situation  in  a  plane  according  to  the  test 
referred  to  above  may  be  ascertained  by  the  observer  moving  his 
head  from  side  to  side  while  the  eye  under  examination  fixes  an  ob- 
ject in  any  given  direction  (preferably  one  straight  in  front).  All 
opacities  in  the  media  of  the  eye  are  either  anterior  or  posterior  to 
the  plane  of  the  iris.  If  the  opacity  is  anterior  to  the  plane  of  the 
iris,  that  is,  in  the  cornea,  it  will  appear  to  move  in  a  direction  oppo- 
site to  that  in  which  the  observer  moves  his  head,  or  is  as  we  say ' 
against  the  movement  of  the  head. 

If  the  opacity  is  in  the  plane  of  the  iris,  that  is,  at  the  anterior  pole 
of  the  crystalline  lens,  it  apparently  does  not  alter  its  position  when 
the  head  is  moved.  If  in  the  vitreous,  however,  behind  the  plane  of 
the  iris,  it  will  appear  to  move  in  the  same  direction  as  that  in  which 
the  head  of  the  observer  moves,  and  will  finally  disappear  behind  the 
iris  on  the  same  side.  The  illustration  of  this  parallactic  displace- 
ment is  simple.  Take  two  pencils  and  hold  them  in  front  of  the  eyes, 
the  one  behind  the  other  and  a  few  inches  apart.  First  let  the  pos- 
terior pencil  represent  the  plane  of  the  iris,  and  the  anterior  one  an 
opacity  in  the  cornea,  anterior  to  this  plane.  Holding  the  pencils  still, 
move  the  head  from  side  to  side.  The  anterior  pencil  appears  to 
move  in  the  opposite  direction  from  the  head.  Now  let  the  posterior 
pencil  represent  the  opacity  and  the  anterior  one  the  iris.  This  time 
when  the  head  is  moved  from  side  to  side  the  posterior  pencil  ap- 
pears to  move  with  the  head. 

Let  a,  b,  c,  d  and  e  be  opacities  in  the  cornea,  at  the  anterior 
pole  of  the  lens,  center  of  lens,  posterior  pole  of  lens  and  in  the 
vitreous  respectively.  An  observer  at  O  sees  them  all  as  occupy- 
ing the  center  of  the  pupil.  As  he  moves  his  eye  down  to  0\ 
capacity  a  appears  to  move  up,  that  is,  it  is  projected  upon  the 
plane  of  the  iris  on  the  opposite  side  of  the  pupil,  b,  occupying 
the  center  of  the  pupil  and  in  the  plane  of  the  iris,  does  not  ap- 
pear to  change  its  position,  c,  d  and  e  appear  to  move  with  the 
head  of  the  observer,  and  finally  get  out  of  sight  behind  the  iris  on  the 


122 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


same  side  of  the  pupil.     At  position  O',  e  has  gotten  out  of  sight 
behind  the  iris,  and  at  O" ,  c,  d  and  e  are  out  of  sight.     The  quicker 

an  opacity  gets  out  of  sight  be- 
hind the  iris,  moving  with  the 
head  of  the  observer,  the  further 
back  in  the  vitreous  is  it  located. 
The  examiner  sees  the  same  por- 
tion of  the  eye-ground  when  he 
moves  his  head  to  the  right  or  to 
the  left  by  the  indirect  as  he  does 
by  the  direct  method  of  ophthal- 
moscopy. Starting  with  the  en- 
trance of  the  optic  nerve  in  view 
with  the  direct  method,  the  observer  moves  his  head  to  the  right. 
He  thus  brings  into  view  a  portion  of  the  retina  to  the  left  of 
the  optic  nerve.  The  nerve  has  moved  out  of  the  field  to  the  right 
of  the  observer.  The  image  moves  with  the  observer.  In  the  in- 
direct method,  with  the  image  of  the  nerve  in  view,  when  the  ob- 
server moves  his  head  to  the  right,  he  sees  the  same  portion  of  the 
retina  that  he  saw  when  using  the  direct  method.  Being  to  the 
left  of  the  nerve  its  image  appears  to  the  right  of  the  nerve  (as 
everything  is  inverted  by  the  indirect  method).  The  nerve  thus 
appears  to  have  moved  towards  the  left,  or  in  a  contrary  way  to 
teh  observer's  head. 

The  ophthalmoscopic  field  is  larger  in  the  indirect  examination  of 
the  fundus  than  in  the  direct ;  that  is,  the  amount  of  retina  or  fundus 
that  can  be  seen  at  once  is  greater  by  the  indirect  method.  The  fol- 
lowing diagrams  explain  the  construction  of  the  ophthalmoscopic 
fields  according  to  Helmholtz. 

FIELD    BY   THE    DIRECT    METHOD. 

The  field  is  constructed  by  drawing  lines  from  the  center  of  the 
pupil  of  the  observer's  eye  to  the  borders  of  the  pupil  of  the  ob- 
served eye,  and  then  continuing  them  as  if  they  were  rays,  through 


OPHTHALMOSCOPY    AND    OBLIQUE    ILLUMINATION.  1 23 

the  dioptric  media  of  the  eyeball.     Of  course,  being  divergent  when 
they  enter  the  eyeball,  they  will  not  be  brought  to  a  focus  until  they 


Observed 


come  to  the  point  C .  As  will  be  seen  the  field  or  the  extent  of  the 
fundus  illuminated  is  greater  in  the  hyperopic  and  less  in  the  myopic 
eye  than  in  the  emmetropic,  if  the  observing  eye  is  beyond  the  prin- 
cipal focal  point  of  the  eye  which  is  nearly  always  the  case.*  As  it 
is  the  pupil  that  limits  the  field  of  view,  we  can  enlarge  the  field  by 
instilling  a  mydriatic  into  the  observed  eye. 

This  deduction  is  an  example  of  inverse  reasoning  that  is  so  often 
used  in  optics.  We  imagine  that  the  pupil  of  the  observer's  eye- 
ball is  luminous  and  we  see  how  much  of  the  fundus  of  the  observed 
eyeball  it  can  illumine.  The  result  is  the  same  on  account  of  the 
reversibility  of  the  process.  The  field,  as  shown  in  the  figure  above, 
is  really  a  little  smaller  than  the  real  field  —  as  to  be  accurate  we 
would  not  construct  C  the  image  of  the  one  point,  C  of  the  pupil  of 
the  observing  eye,  but  the  image  of  the  entire  pupil,  or  rather  of  the 
sight-hole  of  the  ophthalmoscope,  which  would  bring  points  now  lying 
upon  the  edge  of  the  field,  as  constructed  above  well  into  the  field. 

FIELD    BY    THE    INDIRECT    METHOD. 

The  field  by  the  indirect  method  is  constructed  as  follows  :  So  that 
the  field  may  be  as  large  as  it  is  possible  to  make  it  by  the  indirect 
method,  the  objective  lens  should  be  held  at  a  distance  from  the  ob- 
served eye  equal  to  its  focal  diststnce.  The  field  then  occupies  the 
entire  objective  lens,  and  the  iris  disappears  from  view.  We  con- 
struct the  field  as  before  by  supposing  the  center  of  the  pupil  of  the 

*  If  the  observer's  eye  is  at  the  anterior  principal  focus  of  the  observed  eye  the  fields  will  be  equal 
in  £,  Hxa^  m,  as  the  rays  including  them  will  be  parallel. 


124  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

observing-  eye  to  be  luminous,  and  ascertaining  what  part  of  the 
fundus  of  the  patient's  eye  it  could  illuminate.     In  the  figure  above 


it  has  been  assumed  that  the  center  of  the  pupil,  c,  coincides  with  the 
nodal  point  of  the  observed  eye.  The  rays  then  that  enter  the  ob- 
served eye  suffer  no  refraction.  It  will  be  noticed  that  the  field,  ab, 
does  not  depend  upon  the  size  of  the  pupil  of  the  observed  eye. 
The  field  is  only  limited  by  the  borders  of  the  objective  lens.  It  is 
therefore  better  to  use  a  large  lens. 

If  the  lens  be  moved  nearer  or  further  away  from  the  eye  it  will  be 
noticed  that  the  field  becomes  limited  by  the  iris  of  the  observed 
eye.  If  the  pupil  is  large  it  is  easier  to  hold  the  lens  just  in 
the  proper  place  for  the  iris  to  disappear.  By  the  indirect  method 
details  of  the  fundus  are  magnified  about  four  times,  while  by  the 
direct  method  they  are  magnified  about  fourteen  times, (provided  no 
projection  of  the  image  behind  the  eyeball  takes  place).  The  amount 
of  magnification  by  either  method  above  that  stated  depends  upon 
the  distance  at  which  the  image  of  the  fundus  is  projected  behind  the 
eye.  The  following  figure  illustrates  the  manner  in  which  the  fundus 
of  an  eye  is  seen,  and  also  what  is  meant  by  projecting  the  image. 

a"  is  the  image  in  the  fundus  of  the  observing  eye  of  the  object  in 
the  fundus  of  the  observed  eye.  According  to  the  laws  of  lenses,  an 
image  and  the  object  are  embraced  between  secondary  axes  of  the 
lens,  that  is  between  lines  passing  diagonally  through  the  optical 
center  of  the  lens.  In  the  above  case  the  image  and  the  object  are 
embraced  by  the  lines  r  and  r\  secondary  axes  to  the  observing  eye 
as  they  pass  through  its  nodal  point.  (The  nodal  point  of  the  eyeball 
is  to  the  eye  what  an  optical  center  is  to  a  lens.) 


OPHTHALMOSCOPY   AND    OBLIQUE    ILLUMINATION. 


125 


For  a  given  sized  image,  a",  on  the  observer's  retina  the  object 
may  then  be  the  size  of  a',  b  or  c,  according  to  the  amount  of  projec- 
tion. With  both  eyes  open  the  picture  of  the  fundus  as  seen  with 
the  ophthalmoscope  can  be  projected  upon  a  screen  placed  back  of 
the  patient's  head  just  as  an  image  in  a  microscope  can  be  projected 
upon  a  piece  of  paper  laid  beside  the  instrument  upon  the  table. 
Both  eyes  should  always  be  kept  open  in  using  any  optical  instru- 
ment, as  the  pressure  of  the  forcibly  closed  lids  of  the  eye  not  in  use, 
acts  deleteriousl'y  upon  the  cornea,  interfering  with  its  nutrition  and 
ofttimes  giving  rise  to  alteration  in  its  curvature,  and  consequent 


Observer  Mirror  Observera 

The  Lens  of  each  Eye  is  omitted  for  Simplicity  of  Figure 


deficient  vision.  It  is  always  the  eye  unused  that  troubles  one  when 
he  is  in  the  habit  of  closing  one  eye.  Again  if  two  eyes  are  not 
used  much  mag-nification  of  the  fundus  is  missed.  Landolt  deter- 
mined  for  accuracy  in  calculating  the  size  of  fundal  lesions,  that  the 
fundus  of  the  eye  is  magnified  twenty  times  when  projected  behind 
the  eyeball  30  cm.  To  facilitate  measurements  and  to  make  a  rec- 
ord of  the  same,  Dr.  Flavel  Tiffany  has  devised  a  tablet  which  is 
checked  off  into  squares  by  parallel  lines,  5  mm.  apart.  There  is  a 
tablet  for  each  eye.  The  tablet  is  placed  at  30  cm.  behind  the 
patient  and  on  the  side  of  the  eye  to  be  examined,  fastened  to  the 
back  of  his  chair  or  held  by  a  holder  upon  a  table  by  his  side.  At 
first  it  is  difficult  to  project  the  image  of  the  fundus  of  the  eye  under 


126 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


examination  upon  the  card,  but  a  little  practice  will  soon  bring  it  out. 
When  examining  either  eye  it  helps  to  have  the  patient  look  a  little 
in,  towards  the  nose,  and  for  the  observer  to  view  the  fundus  from 
within  outwards.  At  first  the  image  is  seen  projected  upon  the 
cheek  of  the  patient,  but  on  having  him  look  out  a  bit,  the  image 
will  shift  from  the  cheek  to  the  tablet  or  card.  With  the  card  it  is 
easy  at  once  to  determine  the  size  of  an  object  in  the  fundus  of  the 
eye,  and  the  distances  apart  of  different  portions  of  the  retina  or  of 
diseased  areas  in  the  fundus.  Thus :  If  a  lesion  is  seen  to  cover  a 
space  of  I  cm.  upon  the  card  when  projected  upon  it  by  the  observer, 
it  has  .5  mm.  actual  size,  and  so  on. 

The  numerical  value  given  to  ophthalmoscopic  magnification  upon 
the   preceding   page   is  obtained   by  comparing   the  retinal  image 

formed  in  the  observing  eye 
with  the  retinal  image  that  the 
eye  would  have  of  the  same 
object  if  placed  free  in  the  air 
at  the  usual  working  distance 
of  the  observer.  In  the  fol- 
lowing calculation  let  us  sup- 
pose that  the  eye  of  the  observer,  as  well  as  that  of  the  patient,  is 
emmetropic.     For  the  direct  method  the  deduction  is  as  follows : 

A'B'  is  the  image  in  the  fundus  of  the  observer's  eye  of  the  object 
AB,  in  the  fundus  of  the  observed  eye.  Let  AB  be  equal  to  O, 
and  A'B'  to  /,  being  included  between  parallel  lines. 

In  each  eyeball  a  ray  is  drawn  from  either  extremity  of  the  object 
or  image  parallel  to  the  optic  axis.  Therefore,  after  refraction  these 
rays  will  pass  through  the  anterior  focal  point  of  the  eyeball.  As 
both  eyes  are  considered  emmetropic,  their  anterior  focal  distances 
are  equal,  that  is,  00'=  O'l.     In  the  triangles  C(9'Z>  and  C'O'D' 


Observed 


Observer 


(0 


O     F, 


or  /=  O.     The  fundus  of  the  observed  eye  forms  in  the  observing 


OPHTHALMOSCOPY   AND   OBLIQUE   ILLUMINATION.  12/ 

eye  an  image  equal  to  itself.  By  placing  the  fundus  of  the  eye  in 
the  air  at  a  working  distance  of  20  cm.  the  retinal  image  /'  of  the 
object  O  is  easily  found  by  the  formula  Oj I'  =  Dj d=  200] d.  (This 
formula  means  that  the  size  of  the  object  is  to  the  size  of  its  image 
as  the  distance  of  the  object  from  the  anterior  focal  point  of  the  eye 
is  to  the  distance  of  image  from  the  anterior  focal  point.) 
d=  /\,  the  anterior  focal  distance — 

200  mm. 
(2)  .:0/I'  =  — -p^ — . 

Multiplying  two  by  one  we  obtain  the  amount  of  magnification  — 

^      /       200  , 

G  =  ^  =  ^=i3+- 

The  formula  of  magnification  for  any  distance  is 

The  amount  of  magnification  of  the  image  by  the  indirect  method, 
if  we  use  an  objective  lens  of  about  13  D.,  is  four  to  five  times. 


Objective  Len» 


A  B  and  A  B— Object;  C  D     Image. 
At  —  Ant.  Focal  Point  of  Eyeball. 
OC- Focal  Length  of  Objective  Lens. 


The  rays  of  light  from  the  head  of  the  object  AB  in  the  fundus  of 
the  observed  eyeball  pass  out  of  the  eyeball  parallel  as  the  eye  is 
considered  emmetropic.  (The  rays  start  from  the  retina  which  lies 
at  the  principal  focus  of  the  dioptric  system  of  the  eye.)  One  of  the 
returning  rays,  the  one  parallel  to  the  optic  axis,  passes  through  the 


128  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

anterior  focal  point  of  the  eyeball,  and  the  other  one  without  refrac- 
tion through  the  optical  center  of  the  objective  lens.  In  triangles 
A'B'F'  and  OCD,  we  have  this  relation  : 

CD  ^   0C_         I  _0C 
A'B'      B'F"  °''  O      F\ 

!_']']  mm,  _      , 

O      15  mm.      ^ 

If  a  weaker  objective  lens  is  used  the  image  is  situated  at  a  greater 
distance  from  the  lens,  and  is  at  the  same  time  larger.  The  observer 
must  then  use  more  accommodation  to  see  it,  move  further  back  or 
use  a  convex  spherical  lens  back  of  the  sight-hole  of  his  ophthalmo- 
scope. If  a  convex  lens  is  used  in  the  ophthalmoscope,  and  the 
observer  approaches  the  image  of  observed  eye  closer  than  the  focal 
length  of  the  lens  in  use,  the  image  will  be  seen  much  magnified. 
(A  convex  spherical  lens,  when  held  nearer  to  an  object  than  the 
principal  focus  of  the  lens,  magnifies  the  object.)  If  the  observed  eye 
is  myopic,  the  image  of  the  fundus  is  smaller  than  in  the  E.,  and  if 
hyperopic,  larger.  In  emmetropia  the  image  of  the  fundus  of  the  ob- 
served eyeball  is  formed  at  the  principal  focus  of  the  objective  lens 
as  the  rays  of  light  from  the  object  pass  into  the  lens  parallel.  If  the 
eye  is  myopic  the  light  returns  from  it  in  converging  paths,  and  en- 
tering the  lens  is  focused  anterior  to  the  principal  focus,  hence  the 
image  is  smaller,  while  in  hyperopia  the  light  passes  from  the  eyeball 
divergent  and  is  focused  by  the  objective  lens  posterior  to  its  focal 
point,  making  the  image  larger  than  that  of  the  emmetropic  eye. 

After  cataract  extraction,  when  the  eye  has  been  rendered  very 
hyperopic  by  the  removal  of  its  lens,  the  magnification  of  the  fundus 
is  extreme,  and  its  image  is  formed  at  a  great  distance  from  the  ob- 
jective lens.  To  see  this  image  the  observer  must  move  back  or  use 
a  stronger  objective  lens,  say  an  18  D.  S. 

AutO'Ophthalmoscopy .  —  The  examination  of  one's  own  eye-ground 
is  of  limited  utility.     The  method  is  especially  useful  to  those  who 


OPHTHALMOSCOPY   AND   OBLIQUE   ILLUMINATION.  1 29 

are  studying  fundus  details,  without  any  model  save  their  own  eye. 
The  simplest  method  of  seeing  the  interior  of  one's  own  eyeball  is 
that  of  Coccius.*  A  plane  mirror  with  a  large  sight-hole  is  held  in 
front  of  the  eye  so  that  the  light  will  shine  into  the  eye  through  the 
central  hole  of  the  mirror.  The  emergent  rays  of  light  are  caught  by 
the  margins  of  the  opening  in  the  mirror  and  reflected  back  into  the 
eye  upon  the  macula  lutea.  The  image  of  the  fundus  will  be  pro- 
jected by  the  observer's  eye  upon  the  background  behind  the  source 
of  light.  This  is  not  a  mere 
suggestion  as  are  the  images 
of  Purkinje,  but  can  be  seen 
and  reproduced  in  good  de- 
tail. 

Light  a  entering   the  eye 
throup^h  sisfht-hole  of  mirror     ' r^ -^  s^  Projected  image 

of  O.P. 

falls  upon  optic  papilla  and  is         °''*"'  ''^'""^ 

reflected  back  along  path  b  ;  impinging  upon  mirror,  it  again  enters 
the  eye  along  path  c.  The  macula  then  sees  an  image  of  the  nerve- 
head  behind  mirror. 

Ophthalmoscopy  by  Direct  Sunlight  (Jackson).  — For  ordinary  oph- 
thalmoscopic examination,  direct  sunlight  is  manifestly  unfit,  but  for 
certain  diagnostic  purposes  it  is  superior  to  light  from  any  other 
source.  Its  intensity  gives  it  a  greater  penetrating  power  than  any 
other  form  of  light  when  the  media  are  hazy  or  partially  opaque. 
There  is  little  or  no  danger  to  the  eye  from  concentrating  the  intense 
light  and  heat  of  the  sun  upon  the  eye.  The  accurate  focusing  of 
the  light  upon  the  retina  is  prevented  and  even  a  slight  haziness  of 
the  media  renders  impossible  such  a  concentration  of  the  light  as  ex- 
perience has  shown  to  be  injurious.  The  pupil  must  be  dilated  or 
unresponsive  to  the  light  thrown  into  the  eye.  It  is  not  necessary  to 
have  a  dark  room.     The  patient  sits  with  his  back  to  the  sunshine 

*  The  manner  of  performing  autoophthalmoscopy  by  the  indirect  method  has  been  described  on 
previous  page. 


130  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

which  enters  a  window,  or  which  is  reflected  into  the  room  by  a  mir- 
ror outside  of  the  window. 

To  examine  the  anterior  segment  of  the  eye,  the  mirror  is  held 
so  that  the  Hght  is  focused  a  little  anterior  to  the  eye.  To  study 
the  vitreous  or  the  fundus  the  mirror  is  held  so  that  the  light  is 
focused  somewhere  in  the  vitreous  chamber.  The  important  point 
is  to  avoid  concentrating  the  light  upon  the  skin  of  the  face  or 
upon  the  coats  of  the  eyeball.  At  times  better  results  are  ob- 
tained by  not  looking  through  the  hole  in  the  mirror  but  a  little  to 
one  side  of  it.  Or  it  may  be  best  to  illuminate  the  eye,  by  concen- 
trating the  light  (not  focusing  it)  upon  the  sclera  and  then  view  the 
interior  of  the  eye  through  the  pupil.  Examination  of  the  eye  by 
means  of  direct  sunlight  as  outlined  is  of  value  in  cataracts  and  in 
cases  with  cloudy  cornea  and  in  diagnosing  the  presence  of  tumors 
within  the  eyeball,  etc. 

As  an  auxiliary  in  diagnosing  lesions  of  the  fundus  of  the  eye, 
Neuschuler  has  introduced  ophthalmo-chromoscopy.  He  accom- 
plishes this  by  placing  a  series  of  glasses  of  different  colors  behind 
the  sight-hole  in  the  ophthalmoscope.  In  the  application  of  his 
method  he  makes  use  of  a  well-known  law  that  when  an  image  of  a 
color  is  viewed  through  colored  media  the  corresporlding  color  of  the 
interposed  media  will  always  appear  pale.  Red,  green  and  blue  were 
the  only  colors  he  found  necessary  to  employ.  This  method  gives 
very  valuable  results  when  it  is  desired  to  produce  an  exact  picture 
of  the  fundus.  It  may  also  be  used  in  retinoscopy  as  well  as  in  the 
examination  of  the  throat  and  ear. 

Henocque  employs  spectroscopy  in  studying  the  eye.  By  means 
of  his  ophthalmo-spectroscope  he  claims  to  obtain  readily  the  differ- 
ent spectral  colors  from  the  tissues  of  the  eye. 

Reflections  are  very  annoying  to  the  beginner  in  ophthalmoscopy. 
The  one  that  annoys  most  is  the  reflection  of  the  light  from  the  pa- 
tient's cornea.  Its  perception  is  less  when  one  is  nearer  the  eye  and 
one  can  usually  look  to  one  side  of  it  or  through  its  edge,  but  it  is 
always  present  to  disturb  the  view  of  the  fundus  details  in  a  measure. 


OPHTHALMOSCOPY   AND   OBLIQUE   ILLUMINATION.  131 

Almost  as  annoying  is  the  reflection  of  light  from  the  surfaces  of  the 
objective  lens.  These  however  can  be  shifted  from  the  field  of  view 
by  tilting  the  lens  up  or  down  a  litde.  There  are  other  reflections 
seen  in  the  fundus  of  the  eye  which  will  be  described  under  the  ap- 
pearances of  the  fundus. 

Examination  of  the  Eye  by  Oblique  Illumination  or  Transmitted 
Light.  —  Oblique  illumination  of  the  eye  is  performed  by  focusing 
light  upon  it  by  means  of  a  strong  convex  spherical 
lens  held  close  to  the  eye,  and  between  it  and  the 
source  of  light.  Oblique  illumination  is  useful  in 
searching  for  small  foreign  bodies  in  the  cornea, 
conjunctiva  or  under  the  lids,  and  in  examining 
small  lesions  of  the  cornea.  By  holding  the  lens 
a  little  closer  to  the  eye  the  light  can  be  concen- 
trated upon  the  iris  or  upon  the  crystalline  lens  and 
these  structures  examined  under  good  illumination. 
Opacities  in  the  anterior  portion  of  the  vitreous 
humor  or  a  detached  retina  as  well  as  g-rowths  that      '°°*^"  ^'^    ^^'  ^°^ 

<=>  Lens. 

present  themselves  in  that  region  may  be  studied 
by  means  of  oblique  illumination.     A  second  convex  lens  may  be 
used  to  magnify  the  lesion  revealed  by  oblique  illumination,  being 
held  closer  to  the  eye  than  its  focal  distance. 

Jackson  recently  devised  a  binocular  magnifying  lens  made  of  two 
lenses  ground  in  one  piece,  with  which  the  apparent  relation  of  the 
parts  of  the  eye  is  not  altered  as  it  is  when  viewed  with  one  eye  only. 

The  binocular  magnifier  has  since  been  mounted  with  prisms  in 
tubes,  to  which  the  name  of  stereoscopic  loupe  is  given.  The  instru- 
ment is  held  before  the  eyes  by  a  spring  or  rubber  band  about  the 
head. 

In  detecting  the  presence  of  slight  opacities  in  the  media  of  the 
eyeball  a  plane  mirror  is  very  useful.  The  light  is  reflected  into  the 
eye  from  a  distance  of  about  one  foot,  the  room  being  perfectly  dark 
and  with  the  source  of  light  about  six  inches  behind  the  patient's  head. 
Any  opacity  of  the  media  is  then  seen  to  interrupt  the  homogeneous 


132  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

red  glare  of  the  pupil,  and  the  appearance  of  irregular  astigmatism 
described  under  the  head  of  retinoscopy  may  be  seen,  that  is  the  pupil 
appears  to  be  broken  up  into  areas  of  light  and  shade,  that  move 
some  with  and  some  against  the  direction  of  rotation  of  the  ophthal- 
moscopic mirror.     (See  section  on  Retinoscopy.) 

Oblique  illumination  by  direct  sunlight  will  frequently  enable  one 
to  discern  growths  within  the  eyeball  when  the  media  are  cloudy. 
Great  care  is  needed  not  to  bring  the  light  to  an  accurate  focus 
upon  the  cornea.  The  room  should  be  darkened  and  the  sunlight 
reflected  in  by  a  mirror  held  outside  the  window. 


CHAPTER   VIII 

OPHTHALMOSCOPIC    APPEARANCES    OF    THE    FUNDUS    OF    THE    EYE 

The  color  of  the  normal  eye-ground  varies  from  a  light  pink  in  the 
albino  to  almost  a  slate  color  in  the  black-skin  races.  The  lighter 
tlie  complexion  of  the  individual,  the  lighter  the  color  of  the  fundus. 
The  shade  of  the  fundus  is  due  to  the  amount  of  pigment  in  the 
stroma  of  the  chorioid.  The  overlying  retina  is  transparent  in  nor- 
mal conditions  and  does  not  affect  the  color  of  the  eye-ground.  The 
epithelium  of  the  retina  can  at  times  be  recognized  as  a  finely  gran- 
ular surface,  by  the  direct  method,  especially  if  the  refraction  is  per- 
fectly corrected.  In  examining  the  fundus  there  are  two  regions  of 
especial  importance,  namely :  the  entrance  of  the  optic  nerve  and  the 
macular  region  of  the  retina.  Each  of  these  regions  should  be  ex- 
amined separately  for  pathological  changes.  To  bring  the  optic  disc 
or  papilla,  as  the  nerve  head  is  called,  into  view  (into  line  of  vision), 
when  using  the  indirect  method  of  ophthalmoscopy,  the  eye  under 
examination  must  be  turned  towards  the.  nose  about  fifteen  degrees, 
as  the  optic  nerve  enters  the  eyeball  about  fifteen  degrees  to  the 
nasal  side  of  the  center  of  the  retina.  As  the  front  of  the  eyeball 
moves  in  towards  the  nose  the  posterior  portion  moves  out,  bringing 
the  nerve  head  in  line  of  sight  for  the  examiner's  eye.  If  the  exam- 
iner holds  the  ophthalmoscope  before  the  right  eye,  with  the  handle 
of  the  instrument  horizontal,  the  right  eye  of  the  patient  will  be  ad- 
diicted  to  the  proper  amount  if  he  looks  at  the  uplifted  little  finger 
of  the  examiner's  hand  holding  the  ophthalmoscope.  To  examine 
the  nerve  of  the  left  eye,  the  patient  fixes  the  opposite  ear  of  the  ex- 
aminer. It  makes  little  difference  whether  the  patient  simply  turns 
his  eyes  in  the  required  direction  or  turns  his  head,  so  that  he  fixes 
the  proper  point.     Both  eyes  should  be  trained  to  use  the  ophthal- 

^33 


134  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

moscope.     One  can  tell  whether  the  optic  nerve  is  in  line  of  vision 
or  not  before  putting  up  the  objective  lens. 

It  will  be  noticed  that  when  the  light  is  thrown  into  the  eye  that 
the  pupil  immediately  shuts  up,  and  the  fundus  is  poorly  illuminated, 
evidenced  by  the  dark  color  of  the  reflection  from  the  pupil.  When 
the  patient  directs  his  eye  in  the  proper  direction  for  the  light  to 
fall  upon  the  entrance  of  the  optic  nerve,  the  illumination  becomes 
brighter  and  the  pupil  of  the  eye  dilates,  because  the  nerve  head  is 
of  a  lighter  hue  than  the  surrounding  fundus  and  because  the  nerve 
head  is  a  blind  spot,  so  that  light  falling  upon  it  does  not  stimulate 
the  pupil  to  contract.  The  optic  disc  is  more  or  less  circular  in  out- 
line and  of  a  light  pink  color,  and  from  it  radiate  and  ramify  the 
blood-vessels  of  the  retina.  It  varies  from  1.5  to  1.7  mm.  in  diameter. 
It  is  more  or  less  sharply  defined  from  the  surrounding  darker  col- 
ored chorioid,  by  a  more  or  less  well-defined  black  border,  called  the 
chorioidal  ring.  It  is  formed  by  a  heaping  up  of  the  chorioidal  pig- 
ment at  the  nerve  entrance.  This  ring  may  be  entirely  absent  or 
only  marked  in  part  of  the  circumference  of  the  nerve.  Within  the 
pigment  ring  is  most  frequently  a  well-defined  white  ring,  called  the 
scleral  ring.  The  latter  was  formerly  supposed  to  be  the  white 
sclera  showing  through,  the  chorioid  being  deficient  in  that  locality ; 
but  now  we  know  it  to  be  the  nerve  sheath  or  perineurium,  formed 
of  connective  tissue. 

At  times  the  scleral  ring  is  entirely  absent.  There  is  usually  seen 
within  the  confines  of  the  nerve  and  rarely  extending  to  its  margin  a 
depression  whiter  than  the  rest  of  the  papilla.  This  is  the  physio- 
logical pit  or  excavation.  It  lies  to  the  nasal  side  of  the  center  of  the 
papilla  and  frequently  its  nasal  edge  is  steep  and  overhanging,  while 
the  pit  becomes  shallower  and  finally  reaches  the  level  of  the  rest  of 
the  nerve  in  the  opposite  direction.  The  pit  is  formed  by  the  rapid 
arching  of  the  optic  nerve  fibers  as  they  divide  to  supply  the  different 
parts  of  the  retina.  In  the  bottom  of  the  pit  is  exposed  to  view  the 
connective  tissue  that  supports  the  nerve,  the  lamina  cribrosa, 
which  imparts  the  white  color  to  the  depth  of  the  pit  and  the  in- 


OPHTHALMOSCOPIC   APPEARANCES   OF   THE   EYE. 


135 


terstices  between  the  fibers  of  the  lamina  gives  the  pit  a  stippled 
appearance. 

Through  a  larger  opening  between  the  fibers  of  the  lamina,  called 
porus  opticus,  enters  the  retinal  artery.  The  artery  is  accompanied 
by  its  vein,  lying  to  its  temporal  side.  The  vessels  frequendy  show 
a  bend  in  their  course  as  they  emerge  from  the  pit.  Climbing  up  the 
steep  side  of  the  pit  they  suddenly  come  to  view  after  bending  over 
the  edge  of  it.  The  artery  is  of  a  lighter  color  than  the  vein,  and 
smaller  in  diameter.  Both  have  a  light  streak  running  along  the 
middle  of  their  walls.  This  is  a  reflex  streak,  formed  by  the  reflec- 
tion of  light  from  the  anterior  convex  surface  of  the  column  of  blood 
within  the  vessels.  The  arteries  show  this  streak  more  plainly  than 
the  veins,  due  to  the  lighter  color  of  their  contents. 

Loring's  explanation  of  the  reflex  streak  seen  along  the  course  of 
the  retinal  vessels  is  that  the  light  is  condensed  in  passing  through 
the  column  of  blood  in  them  and  then  reflected  back  by  the  under- 
lying tissue.  Noyes  concurs  in  this  opinion,  as  he  noted  a  case  in 
which  there  was  a  hemorrhage  beneath  a  retinal  vessel  that  did  not 
interfere  with  the  continuity  of  the  vessels  but  abolished  its  reflex 
streak.  And,  again  that  in  cases  in  which  a  retinal  vessel  was  seen 
to  cross  an  area  of  fatty  degeneration  in  the  retina  that  the  reflex 
streak  was  intensified  by  the  glistening  surface  beneath  the  vessel. 
Dimmer  thinks  that  the  reflex  in  the  veins  is  due  to  a  reflection 
from  the  surface  of  the  column  of  blood  within  them,  but  that  in  the 
arteries  it  is  from  the  axial  part  of  the  blood  stream.  This  reflex 
streak  differentiates  the  retinal  vessels  from  the  flat  ribbon-like  vessels 
of  the  chorioid,  which  are  also  told  by  their  free  anastomosis. 

At  times  artery  and  artery  or  vein  and  vein  anastomose  upon  the 
surface  of  the  papilla  or  after  leaving  it.  The  arteries  of  the  retina 
are  end  arteries  like  those  of  the  brain  and  kidney.  The  artery 
and  vein  often  cross  and  recross  each  other,  and  if  the  vessel  walls 
are  not  thickened  by  a  pathological  change  taking  place  in  them 
the  one  vessel  will  not  obscure  the  other  from  view  as  it  passes 
over  it. 


o 


6  *  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


Pulsation  of  the  retinal  veins  is  not  infrequent,  especially  if  they 
are  large.  Schon  concluded  from  the  study  of  one  case  that  the 
pulsation  in  the  vein  is  communicated  from  the  artery,  as  the  arter)^ 
and  vein  lie  side  by  side  in  the  optic  nerve.  Pulsation  of  the  arteries 
of  the  disc  occurs  in  cases  of  increased  intraocular  tension,  and  in 
diseases  of  the  heart  especially  in  aortic  stenosis  and  inefficiency. 
At  times  there  is  a  small  arterial  twig  seen  to  enter  the  eyeball  through 
the  medulla  of  the  optic  nerve.  Such  branches  are  usually  derived 
from  the  posterior  or  short  ciliary  arteries  that  pierce  the  sclera  around 
the  optic  nerve  to  supply  the  chorioid  coat.  They  are  called  aberrant 
or  cilio-retinal  arteries  Cilio-retinal  arteries  are  oftenest  seen  in  eyes 
with  myopic  crescents,  and  are  destined  to  nourish  the  tissue  about 
the  macula  lutea. 

The  retinal  vessels  run  chiefly  upwards  and  downwards,  branching 
in  an  arborescent  fashion.  At  the  entrance  of  the  optic  nerve  the 
following  points  are  to  be  considered  :  A  pink  medullary  portion  of 
the  nerve,  a  white  physiological  pit,  vessels  radiating  from  the  pit, 
white  scleral  ring,  black  chorioidal  ring. 

There  are  many  variations,  within  physiological  limits,  in  the  form 
and  appearance  of  the  optic  papilla.  Its  border  may  be  well  defined 
with  a  chorioidal  or  scleral  ring  or  with  both.  Either  ring  may  be 
marked  only  in  pait  of  the  circumference  of  the  nerve,  or  entirely 
absent.  The  edge  of  the  nerve  may  be  rather  illy  defined,  denoted 
simply  by  an  abrupt  change  in  the  color  of  the  fundus.  There  may  be 
no  physiological  pit,  and  the  vessels  not  infrequently  spring  from 
about  the  center  of  the  medullary  portion  of  the  disc.  The  disc  is  to 
be  considered  normal  if  it  is  of  a  clean,  clear,  pink  hue  and  if  its  edge 
is  to  be  readily  discerned,  and  if  the  vessels  upon  its  face  are  clear 
and  well-defined.  The  macula  lutea,  or  area  of  most  distinct  vision, 
is  the  most  important  part  of  the  retina.  It  is  about  2  mm,  in  diam- 
eter and  situated  near  the  posterior  pole  of  the  eyeball.  It  is  difficult 
to  see,  as  the  pupil  shrinks  to  its  smallest  when  the  macular  region  of 
the  fundus  is  illuminated,  and  the  corneal  reflex  is  most  annoying 
when  the  eye  is  in  position  for  viewing  the  macula.     The  macula 


OPHTHALMOSCOPIC   APPEARANCES   OF   THE   EYE.  137 

lutea  or  yellow  spot  was  so  named  from  the  yellow  color  that  it  pre- 
sented in  dissection.  The  yellow  color  is  now  believed  to  be  a  post- 
mortem change.  The  position  of  the  macula  is  marked  in  the  living 
eye  by  a  darker  red  spot  in  the  fundus  with  a  shifting  reflex.  The 
foveal  reflex  is  an  inverted  image  formed  by  the  concave  surface  of 
the  excavation  or  central  pit  of  the  macula,  and  has  the  shape  of  the 
illuminated  area  of  the  ophthalmoscope.  The  reflex  is  annular  if 
the  sight-hole  of  the  ophthalmoscope  is  exactly  centered  with  the 
pupil  of  the  observed  eye,  elliptical  or  comet-shaped  if  the  sight-hole 
and  pupil  are  decentered.  Around  the  macula  the  retina  grows 
gradually  thinner.  This  sloping  of  the  retina  gives  back  a  reflection 
in  the  form  of  a  halo  or  ring  of  smoke  surrounding  the  macula. 

This  ring  is  complete  only  when  the  sight-hole  of  the  mirror  and 
the  pupil  are  centered.  This  reflex  is  seldom  well  seen  by  the  direct 
method.  The  ring  is  usually  horizontally  oval,  and  slightly  larger 
than  the  optic  disc  in  diameter,  and  one  or  two  disc  diameters  from 
its  lower  margin.  These  reflections  are  best  seen  with  a  concave 
mirror,  and  they  change  in  shape  and  distinctness  as  the  focusing  of 
the  light  upon  the  retina  is  altered  by  shifting  the  objective  lens 
backward  and  forward.  This  fact  will  enable  the  beginner  to  differ- 
entiate them  from  infiltrations  into  the  retina,  for  which  they  are  often 
taken.  These  reflections  become  dim  with  old  age.  There  is  not 
infrequently  seen,  especially  in  dark-colored  eyes  and  in  those  of 
children,  a  shimmering  or  watered  silk  appearance  along  the  course 
of  the  retinal  vessels. 

These  reflections  change  with  each  motion  of  the  mirror.  They 
move  against  the  rotation  of  the  mirror  and  thus  show  that  they  are 
reflections  from  concave  surfaces,  where  the  contour  of  the  vessels 
pass  into  the  retinal  level.  There  is  a  reflex  of  the  same  nature  at 
times  seen  parallel  to  the  nasal  side  of  the  papilla  The  macular 
region  of  the  retina  has  very  few  vessels  while  its  central  portion  has 
none  at  all,  by  which  it  may  be  recognized  with  the  ophthalmoscope. 
Pathological  changes  are  frequent  in  this  locality.  The  peripheral 
portions  of  the  retina  have  no  especial  peculiarities.     The  periphery 


138  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

is  at  times  the  seat  of  the  earliest  pathological  changes,  as  in  retinitis 
pigmentosa.  In  the  periphery  of  the  fundus,  the  chorioid  is  often 
thinner  than  elsewhere,  exposing  to  view  its  deeper  layer  of  vessels, 
which  are  seen  running  as  flat  ribbon-like  vessels  of  a  dark  red  color 
and  frequently  anastomosing.  There  is  not  infrequently  a  heaping 
up  of  the  chorioidal  pigment  in  the  periphery  likewise,  giving  it  a 
mottled  appearance. 

In  fair  eyes  the  vessels  of  the  chorioid  are  seen  as  darker  colored 
streams  enclosing  lighter  colored  areas,  while  an  abundance  of  pig- 
ment in  the  chorioid  causes  the  vessels  to  appear  lighter  in  color  than 
the  intervascular  tissue,  especially  if  the  retinal  pigment  epithelium 
is  thin.  Such  a  fundus  is  called  a  tesselated  fundus.  A  thick  retinal 
pigment  gives  the  fundus  a  more  homogeneous  appearance.  In  some 
eyes  the  beginnings  of  the  venae  vorticosse  are  recognizable. 

Differences  in  the  level  of  the  fundus  are  made  apparent  by  the  in- 
direct method  by  parallactic  displacement.  The  convex  lens  (objec- 
tive lens)  is  moved  a  little  up  or  down  during  the  examination.  If  the 
parts  of  the  fundus  in  the  field  occupy  the  same  plane  they  do  not 
alter  their  relative  position  to  each  other  as  the  objective  lens  is  moved. 
If  to  the  contrary  there  exists  a  difference  of  level  between  them  we 
will  see  them  approach  and  recede  from  each  other,  as  the  lens  is 
moved.  By  the  direct  method  of  ophthalmoscopy  we  determine  the 
exact  difference  in  level  of  two  portions  of  the  fundus,  by  ascertain- 
ing the  amount  of  refraction  error  produced  by  the  elevation  of  exca- 
vation.    The  former  gives  rise  to  hyperopia  and  the  latter  to  myopia. 


CHAPTER  IX 

FUNCTIONAL    TESTING.       THE    FIELD    OF    VISION 

Inasmuch  as  functional  testing  is  subjective  entirely,  we  are  de- 
pendent upon  the  intelligence  and  good  will  of  our  patients  for  a 
correct  test.  In  children  and  mentally  deficient  individuals  the  facts 
derived  from  functional  testing  are  frequently  misleading.  When  we 
look  at  an  object  we  can  recognize  its  form,  its  color  and  its  bright- 
ness. The  first  is  called  the  form  sense  ;  the  second,  the  color-sense  ; 
and  the  third  the  light-sense.  These  three  faculties  are  resident  in 
the  retina  throughout  its  entire  extent,  but  to  a  varying  degree, 
and  diminish  from  the  center  to  the  periphery.  Central  vision  is  that 
performed  by  means  of  the  macula  lutea,  and  when  we  look  directly 
at  an  object  we  employ  direct  or  central  vision,  and  the  eye  is  said 
to  have  fixed  the  object.  We  employ  central  vision  for  all  useful 
seeing,  as  when  we  read,  work  or  what  not.  It  is  in  regard  to  the 
central  vision  that  we  test  and  correct  refraction  errors,  and  estimate 
the  amount  of  accommodation  and  visual  acuity.  Peripheral  or  in- 
direct vision  is  that  performed  by  other  portions  of  the  retina.  Indi- 
rect vision  is  poorer  for  form,  color  and  light  the  further  from  the 
center  vision  is  performed.  The  extent  of  indirect  vision  for  form 
or  space  is  called  the  field  of  vision.  If  we  get  such  poorly  defined 
perceptions  by  indirect  vision,  of  what  use  is  it  at  all  ? 

A  person  devoid  of  peripheral  vision  is  in  the  same  condition  as 
one  looking  through  a  long  narrow  tube.  He  can  read  the  finest 
print  straight  ahead  but  is  not  in  a  condition  to  go  about  alone,  as  he 
would  stumble  and  fall  over  everything  in  his  path.  Peripheral  vision 
is  of  value  in  enabling  us  properly  to  place  objects  in  space,  and  thus 
placing  them,  avoid  falling  over  them  or  avoid  colliding  with  them. 
This  faculty  of  assigning  to  objects  their  proper  position  in  space  is 
called  orientation.     While  we  are  walking  along,  a  stone  in  our  path 

139 


140 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


forms  its  image  on  the  periphery  of  our  retinas,  our  attention  is  at- 
tracted to  it  thereby,  and  we  then  turn  our  eyes  directly  towards  it. 
Our  central  vision  then  gives  us  a  clear  conception  of  the  nature  of 
the  obstacle,  and  we  then  avoid  it.  The  same  thing  is  done  when 
moving  objects  approach  us  from  the  side.  Their  images  are  first 
formed  upon  the  periphery  of  the  retina,  which  awakens  our  attention 
to  their  approach.  If  it  were  not  so,  we  would  not  be  able  to  go 
about  in  a  crowded  street  without  being  run  over  by  some  vehicle. 
Exner  has  shown  that  the  peripheral  portion  of  the  retina  has  quite 
a  high  degree  of  sensitiveness  for  the  projection  of  motion  in  an  ob- 
ject, so  that  our  attention  is  attracted  most  certainly  to  it. 

We  refer  an  object  in  space  along  a  line  which  we  imagine  drawn 
from  the  retinal  image  through  the  nodal  point  to  the  outside.  The 
object  and  its  retinal  image  are  then  diametrically  opposite.  The 
upper  part  of  the  retina  is  stimulated  by  an  object  below  the  level  of 
the  eyes  when  the  eyes  are  directed  straight  ahead  and  vice  versa. 

In  the  figure,  let  N  be  the  nodal 
point  of  the  eyeball  AB,  A'B'  and 
A"B",  the  objects  of  attention.  A 
line  drawn  from  the  head  of  each  ob- 
ject through  the  nodal  point  of  the 
eye  will  stimulate  the  retina  at  the 
point  a,  and  likewise  the  tail  of  each  image  will  stimulate  the  retina 
at  the  point  b,  in  the  fundus  of  the  eye.  The  lines  connecting 
different  points  of  the  object  with  like  points  in  the  image  are  called 
visual  axes.  It  will  be  seen  from  the  figure  that  the  image  ab,  cor- 
responds to  either  object,  AB,  A'B'  or  A" B" .  The  distance  of  the 
object  before  the  eyes  is  however  estimated  subjectively  by  the  amount 
of  accommodation  needed  to  bring  it  to  a  sharp  focus  upon  the  retinae, 
and  by  the  amount  of  convergence  necessary  to  see  it  singly  with  the 
two  eyes.  Whenever  the  retina  is  stimulated,  the  stimulation  is  pro- 
jected into  space  along  lines  as  shown  above.  This  is  called  project- 
ing an  object  into  space.  By  virtue  of  this  fact  we  see  the  objects  in 
the  external  world  arranged  in  their  proper  relation  in  regard  to  one 
another  (objective  orientation). 


FUNCTIONAL   TESTING.     THE    FIELD    OF    VISION.  141 

But,  to  get  a  correct  idea  of  the  arrangement  of  objects  in  space, 
we  must  have  a  knowledge  of  the  relation  that  they  bear  to  our  own 
position,  in  space  (subjective  orientation).  The  latter  depends  upon 
us  having  a  correct  idea  of  the  position  of  our  bodies  in  space,  and 
the  position  that  our  eyes  occupy  in  our  heads.  The  former  is  given 
to  us  by  the  sense  of  equilibrium,  through  the  internal  ear  and  the 
cerebellum,  and  the  latter  by  the  muscular  sense  resident  in  the  extra- 
ocular muscles  themselves,  which  informs  us  how  our  eyes  are  turned 
in  our  orbits.  By  means  of  objective  and  subjective  orientation  we 
can  assign  to  an  object  that  is  presented  to  our  view,  its  true  position 
in  space.  As  a  rule  we  see  with  both  eyes  at  once,  but  the  two 
images,  one  upon  each  retina,  are  fused,  i.  e.,  the  stimulation  in  each 
eye  is  conveyed  to  the  brain  and  interpreted  as  one  image  corres- 
ponding to  one  object  in  space  so  long  as  corresponding  parts  of  the 
two  retinas  are  stimulated,  the  macula  lutea  in  each  or  the  same  dis- 
tance to  the  right  or  left,  above  or  below  the  macula  in  each  eye. 

According  to  the  law  of  projection,  when  the  same  part  of  each 
retina  is  stimulated,  the  object  of  stimulation  is  located  by  both  eyes 
at  the  same  point  in  the  outer  world,  and  hence  the  object  is  seen  as 
one  with  both  eyes,  or  there  is  then  single  binocular  vision. 

In  stereoscopic  vision,  or  the  estimation  of  solidity  of  an  object, 
the  portion  of  the  retina  stimulated  in  one  eye  does  not  correspond 
with  that  stimulated  in  the  other  eye,  as  will  be  seen  later  on,  although 
there  is  fusion  of  the  retinal  images,  giving  perspective  to  the  object. 
If  a  prism  be  placed  before  one  eye  so  that  the  light  that  enters  it  is 
deviated  from  its  proper  path  the  eye  will  place  the  object  in  a  faulty 
direction  in  space.  This  is  called  false  orientation.  If  one  eye  is 
turned  out  of  the  line  of  vision  for  the  object  of  attention,  as  in  cases 
of  crossed  eyes,  the  same  thing  happens.  Each  eye  projecting  its 
image  in  a  different  direction  in  space  causes  the  two  eyes  to  see  a 
single  object  as  two.  There  is  binocular  diplopia,  or  double  binocu- 
lar vision.  Diplopia  exists  only  in  cases  of  rather  recent  squints,  for, 
after  the  squint  has  existed  for  a  while  the  patient  learns  not  to  take 
account  of  the  image  formed  in  the  deviating  eye,  as  diplopia  is  very 


142  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

annoying.     There  is  suppression  of  the  retinal  image  in  the  squint- 
ing eye,  as  we  speak  of  it. 

EXAMINATION    OF   THE    FIELD    OF    VISION. 

The  examination  must  be  made  for  each  eye  separately.  The  eye 
under  test  is  kept  fixed  upon  a  point  straight  ahead,  and  the  fellow 
eye  bandaged.  While  the  eye  maintains  central  fixation,  an  object 
is  moved  from  the  periphery  over  the  field  of  view,  or  the  reverse, 
that  is,  beginning  at  the  point  of  fixation  the  object  is  moved  towards 
the  periphery  in  different  directions.  The  simplest  but  at  the  same 
time  a  crude  way  to  estimate  the  extent  of  indirect  vision  is  for  the 
physician  to  place  himself  directly  in  front  of  the  patient,  and  at  a 
short  distance  from  him,  and  then  move  his  uplifted  finger  or  a  small 
white  ball  upon  a  black  rod,  gradually  from  the  periphery  towards 
the  center  and  midway  between  himself  and  the  patient.  The  ex- 
aminer closes  the  eye  that  is  opposite  the  bandaged  one  of  the  patient. 
The  patient  is  instructed  to  say  so  as  soon  as  he  sees  the  hand  or  the 
object  approaching.  Taking  it  for  granted  that  the  field  of  the  ex- 
aminer is  normal  this  will  occur  at  the  time  the  physician  himself  first 
sees  the  object  approaching,  if  the  limits  of  the  patient's  field  are 
normal. 

The  hand  is  moved  from  either  side  and  from  above  and  below, 
and  the  point  at  which  the  physician  and  the  patient  see  the  hand  for 
the  first  time  compared.  Small  defects  in  the  visual  field  are  not 
recognized  by  this  method.  It  is  the  only  way  that  we  can  test 
patients  with  deficient  visual  acuity,  and  in  cataract  cases,  where  the 
vision  is  still  better  than  the  perception  of  light  only,  but  when 
smaller  test  objects  can  no  longer  be  distinguished.  The  field  is  to 
be  gotten  more  accurately  upon  a  blackboard,  but  with  considerable 
inconvenience.  We  place  the  person  in  front  of  a  blackboard  at  a 
distance  of  25  cm.,  which  distance  must  be  maintained  throughout 
the  test.  Directly  in  front  of  the  patient's  eye  we  make  a  mark  on 
the  board,  which  he  is  to  fix  during  the  examination.  A  stick  of 
white  chalk  is  now  gradually  brought  from  the  edge  of  the  board 


FUNCTIONAL   TESTING.     THE   FIELD   OF   VISION.  143 

towards  the  center,  and  the  point  at  which  it  first  comes  into  view  ir 
marked.  By  thus  marking  the  Hmits  of  the  vision  in  every  direction, 
and  connecting  the  points  by  straight  hnes  we  outHne  the  extent  of 
indirect  vision.  The  size  of  the  field  as  depicted  upon  the  board  is 
of  course  dependent  upon  the  distance  of  the  patient  from  the  board. 
If  we  divide  the  board  up  into  squares  of  i  cm.  each,  and  have  the 
patient  at  exactly  25  cm.  from  the  point  of  fixation,  the  value  in  de- 
grees of  arc  of  the  squares  on  the  plane  surface  may  be  ascertained 
from  the  following  table  : 


2.2  cm. 

5 

degrees. 

17-5 

cm. 

35  degrees. 

4.4 

10 

21 

40 

^.7 

15 

15 

45 

9.1 

20 

30 

50 

II. 7 

25 

36.7 

55 

14.4 

30 

33-3 

60 

This  method  is  a  very  imperfect  one.  due  to  the  fact  that  it  is  im- 
possible to  project  a  hollow  sphere  upon  a  plane.  Equal  distances 
upon  the  plane  correspond  to  unequal  distances  upon  the  retina. 
The  second  evil  is  that  the  whole  field  cannot  find  a  place  upon  a 
plane.  The  normal  field  extends  on  the  temporal  side  to  ninety  de- 
grees and  even  beyond ;  therefore,  the  temporal  limits  of  the  field  can 
never  be  projected  upon  a  plane.  The  figure  illustrates  each  of 
these  points. 

In  the  figure  the  eye  E  is  represented  as  fixing  the  point  F.  Points 
a,  b  and  c  are  equidistant  along  the  horizontal  plane  LL' .  The 
dotted  lines  aa"  and  bb"  are  drawn  through  the  nodal  point  of  the 
eye  without  any  refraction,  as  they  enter  the  dioptric  media  of  the 
eyeball ;  points  a"  and  b"  would  then  be  the  areas  of  stimulation 
from  the  objects  a  and  b  respectively,  but  refraction  takes  place  in 
rays  from  a  and  b,  as  they  enter  the  eyeball ;  ergo :  point  a"  is  shifted 
to  point  a',  and  point  b"  to  b\  the  true  positions  of  the  retinal  images 
of  the  objects  a  and  b.  Intervals  Fa,  ab  and  be  are  equal,  but  the  in- 
tervals corresponding  to  them  upon  the  retina  are  unequal,  i.  e.,  Fa\ 


144 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


a'b'  and  b'c'  are  unequal,  diminishing  towards  the  periphery.  Point 
d  2X2,  right  angle  with  the  visual  axis  FF\  can  stimulate  the  retina 
as  the  light  from  it  undergoes  a  sharp  bending  as  it  enters  the  diop- 


Macula 


trie  media  of  the  eye,  and  so  the  light  passes  into  the  eyeball  through 
the  pupil.  As  LL'  and  od  are  parallel,  point  d  can  have  no  place 
upon  the  plane  LL' ,  therefore  the  whole  field  of  vision  cannot  be 
projected  upon  a  plane. 

There  is  only  one  way  to  properly  represent  the  visual  field,  and 
that  is  to  project  it  upon  a  hollow  sphere  (Aubert).  ,The  instrument 
employed  thus  to  take  the  field  of  vision  is  called  a  perimeter.  There 
are  many  different  types  on  the  market,  but  all  are  constructed  so 
that  the  field  is  projected  upon  an  arc,  the  section  of  a  hollow  sphere, 
that  can  be  rotated  in  different  meridians.  In  most  of  the  instru- 
ments the  test  object  is  moved  along  the  arc  by  the  hand  of  the  op- 
erator, and  when  it  first  comes  into  view,  its  position  is  marked  upon 
a  chart  which  comes  for  the  purpose.  The  latest  improved  instru- 
ments have  a  system  of  gearing  that  enables  the  operator  to  move 
the  test  object  along  the  arc  of  the  instrument  by  operating  a  small 
milled  wheel,  at  the  back  of  the  perimeter.  In  order  to  save  time 
there  is  also  an  arrangement  to  punch  or  mark  the  chart  in  the 
proper  place,  when  the  patient  first  sees  the  approaching  object. 
Several  models  of  perimeters  are  appended. 


FUNCTIONAL   TESTING.     THE    FIELD    OF   VISION. 


145 


Dana's  pocket  perimeter  is  a  very  convenient  one  for  the  oculist 
who  has  to  carry  his  instrument  to  the  bedside  of  an  invalid  or  sick 
patient,  or  for  one  who  visits  many  institutions.    This  instrument  con- 
sists of  a   metal  semi-circular 
protractor,  graduated  from  cen- 
tral o  to  90   degrees    in   both 
directions.      The  movable  bar 
which    carries    the    white    and 
colored  test  objects  rotates  on 
a  pivot  over  the  surface  of  the 
graduated    scale.       To    obtain 
the  field  in   the  horizontal  di- 
rection, the  scale  is  placed  di- 
rectly   under   the  eye,   resting 

the  instrument  against  the  cheek  bone,  and  the  extent  of  the  field  is 
denoted  by  the  position  of  the  bar  upon  the  scale. 

The  vertical  meridian  of  the  field  is  taken  by  resting  the  instru- 
ment against  the  temple  and  reading  in  the  same  manner.  The 
instrument  can  be  easily  carried  in  the  vest  pocket,  by  sliding  the 
extension  rod  into  the  hollow  handle,  the  colored  discs  being  held  by 
a  small  clip  upon  the  reverse  side  of  the  scale.  The  model  that  is 
perhaps  the  most  universally  employed  is  that  shown  in  the  cut 
belOw,  of  which  there  are  various  makes. 

This  instrument  combines  the  most  practical  points  in  the  Landolt 
and  Priestly  Smith  perimeters.  It  has  a  broad  hard-rubber  arc  with 
a  sliding  object  carrier  after  the  pattern  of  Landolt  and  the  register- 
ing attachment  of  the  Priestly  Smith  instrument.  It  has  an  adjustable 
double  chin  rest  sliding  upon  an  upright  bar,  the  end  of  which  carries 
the  cheek  rest.  The  chart  is  fixed  to  a  hard-rubber  disc  attached  to 
the  back  of  the  instrument  and  revolving  with  it.  A  stationary  scale, 
mounted  upon  an  upright  arm,  is  graduated  to  correspond  to  the 
divisions  upon  the  arc,  and  is  placed  immediately  back  of  the  disc 
holding  the  chart.  By  means  of  this  scale  the  exact  position  of  the 
object  upon  the  arc,  and  the  meridian  of  the  arc  itself  is  marked  by  a 


146 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


single  puncture.  To  avoid  orientation  in  the  mind  of  the  examiner 
the  scale  back  of  the  chart  is  graduated  in  two  colors,  red  and  white ; 
the  degrees  on  the  arc  are  likewise  in  red  and  white.  A  simple  ob- 
servation of  the  color  and  degree  on  the  arc  at  which  the  object  stands 
only  is  necessary  to  prick  the  chart  in  the  proper  place.  There  is  an 
opening  through  the  center  of  the  spindle  of  the  arc  to  allow  the  ex- 


o 


Meyrowitz  Perimeter. 

aminer  to  watch  the  eye  of  the  patient,  so  that  central  fixation  is 
maintained  throughout  the  test.  The  color  discs  show  colors  of  white, 
red,  green,  blue  and  yellow  in  squares  of  5  mm.,  and  are  carried  on 
a  handle  45  cm.  long.  The  two  instruments  below  are  self-record- 
ing.    Dr.  Skeel's  is  the  more  complicated  and  more  apt  to  get  out 


FUNCTIONAL  TESTING.     THE    FIELD   OF   VISION. 


^M 


of  order.     The  chart  is  fixed  upon  the  platform,  as  shown  in  the  cut. 
The  knob  on  the  back  of  the  disc  is  rotated,  draw- 
ig  the  object  along  the  arc  until  it  comes  into 
the  field  of  view,  the  lever  at  the  bottom 
of  chart  platform  is  then  pressed  and  the 
chart  is  rnarked  in  the  proper  place. 
In  the  Hardy  instrument  the  chart 
is  fixed  upon  the  disc  that  pro- 
jects from  the  instrument  and 
the  carrier  moved  along  the 
arc   by  rotating  a   milled 
head.     The  chart  is  marked 
in  the  proper  place  by  press- 
ing  the    chart   up   against   a 
needle-point. 

One  should  have  an 

^adjustable  table  for 

the  perimeter  so  that 

it    can    be     placed 

quickly   at  the 

proper  height   for  the 

patient. 

TJie  Extent  of  the  Field 

of  Vision.  — The  normal  field  of 

vision,  as  will  be  seen  by  a  glance 

at  the  accompanying 

figure,  does  not  extend 

equally  far  in  every  direc- 

It  extends  furthest  to 

the    external    or   temporal    side, 

reaching  to  90  degrees  or  even 

^►beyond.     We  can  see  objects  on 

the  temporal  side,  that  is  in  the  tem- 


Hardy  Perimeter. 


poral  field,  even  if  they  lie  a  little 


148 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


posterior  to  a  plane  passing  through  the  pupil.  This  is  on  account 
of  the  strong  refraction  that  the  light  from  such  a  point  undergoes 
at  the  surface  of  the  cornea,  enabling  it  still  to  enter  the  pupil.  The 
field  is  much  less  extensive  to  the  inside  and  to  the  inside  and  be- 
low. The  cause  of  this  is  that  the  nose  and  the  cheek  intercept  vision 
in  these  directions,  but  if  the  head  be  rotated  so  that  these  obstacles 
are  removed,  the  field  will  even  then  be  found  not  to  extend  as  far 
to  the  nasal  side  as  to  the  temporal.  This  is  because  the  retina  does 
not  extend  as  far  to  the  temporal  side  as  to  the  nasal  side  of  the  eye- 
ball, for  it  is  the  nasal  retina  that  sees  objects  in  the  temporal  field 
and  vice  versa.  And  as  Landolt  pointed  out,  the  temporal  retina  is 
not  as  acute  as  the  nasal  portion,  as  it  is  not  used  so  much.  The 
limits  of  the  field  of  vision  for  white  in  round  numbers  are  :  Above, 
50°  ;  nasally,  60°  ;  below,  70°  ;  temporally,  90°.  The  color  visual 
fields  are  less  extensive  than  that  for  white.  Blue  is  recognized  at 
the  greatest  distance  from  the  center,  then  yellow,  orange,  red,  green 
and  violet  are  recognized  at  decreasing  distances  from  the  center  in 

the  order  named.  The  blue 
field  is  five  degrees  within 
the  white  one ;  the  red 
ten  degrees  within  the 
blue,  and  the  green  ten  de- 
grees within  the  red  field. 
In  the  figure  the  limits 
of  the  white  area  repre- 
sent the  extent  of  the  field 
of  vision  for  white.  The 
small  circle  near  the  center 
of  each  chart  represents  the  position  of  the  physiological  blind  spot, 
i.  e.,  the  head  of  the  optic  nerve.  The  dotted  line  in  the  left-hand  chart 
is  the  extent  of  the  field  for  blue  ;  the  stroke  and  dot  line,  that  for  red, 
and  the  cross  line,  the  field  for  green.  The  extent  of  the  field  for 
white  and  for  colors  varies  very  much  in  different  individuals  within 
physiological  limits.     If  either  field  is  curtailed  ten  degrees  or  more 


L.E. 


R.E, 


FUNCTIONAL   TESTING.     THE    FIELD    OF   VISION,  1 49 

within  the  limits  given  it  is  to  be  considered  abnormal.  As  we  ordi- 
narily measure  the  visual  field,  as  Baas  pointed  out,  we  measure  the 
relative  visual  field  in  contradistinction  to  the  absolute  field  of  vision. 
The  relative  visual  field  records  the  limits  of  vision  for  an  object  of  a 
definite  size,  while  the  absolute  field  is  the  limit  of  the  field  of  vision 
without  regard  to  the  size  of  the  object.  The  figures  given  above 
represent  the  extent  of  indirect  vision  taken  with  a  test  object  1.5 
cm.  square. 

Pathological  alterations  in  the  field  of  vision  consist  in  its  curtail- 
ment. This  may  be  concentric  (contracted  equally  in  all  directions) 
with  the  retention  of  good  direct  (central)  vision.  When  the  field  is 
much  encroached  upon  the  individual  has  lost  the  faculty  of  orienta- 
tion. At  times  the  contraction  is  more  decided  on  one  side  of  the 
field  than  on  the  other,  as  in  glaucoma,  in  which  the  nasal  field  suffers 
the  greatest  shrinkage.  When  the  contraction  is  in  the  shape  of  a 
triangle  with  its  apex  at  the  center  of  the  field,  it  is  spoken  of  as  a 
sector-shaped  contraction.  The  entire  one  half  of  the  field  may  be 
wanting,  constituting  the  hemianopic  field.  Blind  spots  within  the 
limits  of  the  visual  field  are  called  scotomata.  One  of  these  exists 
in  the  normal  eye  at  the  entrance  of  the  optic  nerve.  It  is  known 
as  Mariotte's  blind  spot.  It  lies  to  the  temporal  side  of  the  point 
of  fixation  about  fifteen  degrees.  The  scotomata  that  occur  as  the 
result  of  disease  are  known  according  to  their  locality  as  central  or 
peripheral.  A  central  scotoma  involves  the  macula  lutea.  The 
patient  with  such  a  blind  spot  can  no  longer  see  fine  print  or  do  fine 
work,  but  is  perfectly  able  to  get  safely  about  alone,  just  the  reverse 
of  one  who  has  a  contracted  field,  with  retention  of  normal  central 
vision.  At  times  there  exists  an  annular  scotoma  around  the  point 
of  fixation,  leaving  the  macula  intact.  Von  Graefe  was  the  first  one 
to  show  the  importance  of  taking  the  field  of  vision  in  eye  practice. 
He  showed  that  many  intraocular  diseases  had  their  peculiar  forms 
of  alteration  in  the  visual  field.  Concentric  contraction  with  reten- 
tion of  normal  or  good  central  vision  is  met  with  especially  in  cases 
of  retinitis  pigmentosa,  less  frequently  in  glaucoma  and  in  atrophy 


150  THE   EYE.    ITS    REFRACTION   AND    DISEASES. 

of  the  optic  nerve.  In  most  cases  of  marked  peripheral  contraction 
of  the  visual  field  central  vision  is  greatly  reduced.  We  find  sector- 
shaped  contraction  especially  in  cases  of  occlusion  of  the  retinal 
artery  and  in  optic  nerve  atrophy.  In  glaucoma  marked  contraction 
of  the  nasal  field  is  of  frequent  enough  occurrence  to  be  of  some 
pathognomonic  importance.  Scotomata  are  most  frequently  to  be 
met  with  in  diseases  of  the  fundus  with  circumscribed  lesions,  there- 
fore in  retinitis  disseminata.  The  blind  spots  in  chorioidal  diseases 
correspond  to  the  lesions  seen  in  the  fundus  of  the  eye  with  the 
ophthalmoscope.  So  long  as  these  spots  are  peripheral  the  vision 
does  not  suffer  to  any  great  extent,  but  if  numerous  the  field  assumes 
a  sieve-like  character.  If  the  cause  of  the  scotoma  is  not  apparent 
in  the  fundus  of  the  eye  it  must  be  looked  for  in  the  optic  nerve. 
Scotomata  are  divided  into  positive  and  negative  scotomata.  By  the 
first  is  meant  a  spot  in  the  field  in  which  objects  are  not  distinctly 
visible,  a  cloud  apparently  being  interposed  between  the  eye  and  the 
object.  If  the  cloud  is  faint  and  does  not  entirely  obscure  the  object 
we  have  a  relative  positive  scotoma ;  while  on  the  other  hand  if  the 
cloud  is  dense  enough  entirely  to  obscure  the  object  of  attention 
from  view,  we  call  it  an  absolute  positive  scotoma. 

Positive  scotomata  are  produced  by  opacities  in  thp  media  of  the 
eyeball  which  throw  their  shadows  upon  the  retina,  or  retinal  exu- 
dates or  hemorrhages  into  the  retina  anterior  to  the  layer  of  percipi- 
ent elements.  As  these  lesions  cast  shadows  they  are  perceived  as 
dark  spots.  If  the  opacities  are  in  the  vitreous  they  are  most  likely 
to  be  mobile,  giving  rise  to  motile  scotomata.  Fixed  scotomata  are 
caused  by  opacities  in  the  cornea,  lens  or  retina.  These  scotomata 
are  best  made  apparent  by  having  the  patient  gaze  upon  a  uniformly 
bright  surface,  as  a  sheet  of  white  paper.  They  will  be  more  appar- 
ent, if  slight,  when  the  illumination  is  reduced.  The  patient  may  be 
instructed  to  outline  the  spot  seen  upon  the  paper  with  a  pencil,  from 
which  the  extent  of  the  diseased  area  can  be  estimated.  If  the  eye 
of  the  patient  is  at  25  cm.  from  the  paper,  and  the  projection  of  the 
scotoma  as  outlined  by  him  upon  the  paper  is  i  cm.  in  diameter,  the 


FUNCTIONAL    TESTING.     THE   FIELD    OF   VISION.  151 

lesion  in  the  fundus  causing  the  blind  spot  is  .06  mm.  in  diameter. 
The  size  of  an  object  and  its  image  are  to  each  other  as  their  respec- 
tive distances  from  the  lens. 

Ij  0  =  djD,     z/io=  15/250  mm.,  z  =  .06  mm. 

A  negative  scotoma  is  simply  a  break  in  the  field,  an  area  in 
which  nothing  is  distinctly  seen,  but  nothing  appears  to  be  interposed. 
If  the  object  looks  pale  but  can  still  be  seen,  there  exists  a  relative 
negative  scotoma,  while  if  the  object  is  not  discernible  in  that  part 
of  the  field  we  have  an  absolute  negative  scotoma.  All  the  percep- 
tion of  light  is  wanting  within  the  confines  of  an  absolute  negative 
scotoma.  Negative  scotomata  are  only  discovered  by  taking  the  field 
of  vision,  with  small  and  especially  with  colored  objects,  for  as  the 
visual  acuity  diminishes,  the  ability  to  distinguish  colors  disappears 
before  the  ability  to  distinguish  form  or  outlines  of  the  object. 

This  is  best  illustrated  in  cases  of  poisoning  from  alcohol  and  to- 
bacco. Such  a  case  examined  with  a  white  test  object  seems  to  have 
a  normal  visual  field,  while  if  a  small  red  or  green  colored  object  be 
used,  there  is  found  a  central  negative  scotoma,  in  which  location  red 
or  green  is  not  recognized  as  such.  The  examination  of  the  field  for 
colors  is  of  great  practical  importance  and  too  infrequently  done.  It 
not  infrequently  happens  that  the  colored  fields  show  curtailment 
some  time  before  any  change  is  noted  in  the  form  of  the  white  field. 
Rapid  falling  off  of  the  color  fields  is  associated  with  disease  of  the 
optic  nerve  and  soon  leads  to  blindness.  The  charts  used  for  record- 
ing the  field  of  vision  do  not  represent  the  part  of  the  retina  of  the 
eye  under  test  stimulated,  but  the  part  or  location  of  external  space 
in  which  the  test  object  has  become  visible;  so  that  in  marking  the 
chart  when  the  object  is  seen  on  the  temporal  side  of  the  eye,  a  dot 
is  placed  upon  the  chart  on  the  side  marked  temporal.  If  the  chart 
be  held  in  front  of  the  patient  there  can  no  mistake  be  made,  as 
then  all  objects  seen  on  the  right  of  the  eye  will  be  marked  on  the 
right  and  those  on  the  left  on  the  left  side  of  the  chart  in  regard  to 
the  patient.     The  binocular  field  of  vision,  or  that  area  in  which  an 


1^2  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

object  is  simultaneously  visible  to  the  two  eyes,  is  more  or  less  circu- 
lar in  outline.  It  extends  above  to  the 
upper  Hmits  of  the  monocular  field  and  to 
the  extent  of  the  field  of  each  eye  below, 
and  laterally  from  the  fixation  point  to  about 
sixty  degrees.  The  fixation  point  is  the  cen- 
ter of  this  area  and  the  physiological  blind 
s^j^^ '^'^  spot  of  each  eye  on  the  corresponding  side 
p      .""c'lwT  v«u.  of  the  fixation  point.     The  binocular  field 

Binocular  Field  lor  White  r^ 

of  vision  is  not  the  space  in  which  an  object 
is  visible  to  either  eye,  but  that  in  which  the  object  is  visible  to  both 
eyes  at  once.  The  temporal  field  of  each  eye  extends  thirty  degrees 
beyond  the  limits  of  the  binocular  field. 

The  Technique  of  Takmg  a  Field  of  Vision. — Seat  the  patient  in 
front  of  the  perimeter  so  that  his  chin  will  rest  upon  the  chin-rest 
comfortably,  with  the  cheek  pressed  against  the  upright  piece  that 
springs  from  the  side  of  the  chin-rest.  The  curved  top  of  the  cheek- 
rest  should  fit  into  the  depression  under  the  malar  bone.  The  head 
is  directed  straight  forward  and  the  eye  not  under  test  is  bandaged, 
or  closed  by  a  card  held  in  front  of  it  by  the  patient,  care  being  taken 
that  the  card  or  bandage  does  not  rise  above  the  bridge  of  the  nose 
to  occlude  the  vision  in  the  lower  nasal  field.  The  eye  under  the 
test  fixes  the  white  dot  at  the  center  of  the  arc  of  the  perimeter,  and 
throughout  the  test  the  eye  remains  constantly  fixed  upon  this  dot. 
The  test-object  is  then  moved  up  from  the  periphery  and  the  point 
at  which  it  comes  into  view  is  noted  upon  the  chart.  The  arc  of  the 
instrument,  which  up  to  this  time  has  been  in  a  vertical  position,  is 
turned  fifteen  degrees  the  one  way  or  the  other,  and  the  point  at 
which  the  object  is  first  seen  in  this  new  meridian  is  marked.  The 
arc  each  time  is  turned  through  fifteen  degrees,  and  the  limits  of  the 
field  noted  in  each  meridian  of  rotation.  While  the  arc  is  in  the 
same  position,  two  points  may  be  taken,  one  above  and  the  other 
below,  or  to  the  right  or  left  as  the  case  may  be,  and  thus  some  time 
saved.     The  dots  upon  the  chart  are  now  connected  by  straight  lines 


FUNCTIONAL   TESTING.     THE   FIELD    OF   VISION.  1 53 

and  the  field  thus  outlined.  The  color  fields  are  now  taken  in  the 
same  way,  usually  blue,  red  and  green  only  being  selected.  Small 
test-objects  are  used  when  hunting  for  blind  spots.  The  operator 
should  wear  black  gloves  during  perimetric  examination,  so  that  his 
white  hands  and  cuffs  do  not  attract  the  eye  of  the  patient  away  from 
the  point  of  fixation.  It  is  not  necessary  to  do  this  in  the  Hardy  and 
Skeel  instruments  as  the  test-object  is  moved  along  the  arc  by  op- 
erating a  small  milled  head  behind  a  disc  that  hides  the  hand  of  the 
operator  from  view.  If  one  desires  to  study  from  day  to  day  the 
change  in  shape  and  size  of  a  scotoma,  it  can  be  outlined  upon  a 
larger  scale  than  is  usually  done  by  placing  the  patient's  eye  further 
from  the  fixation  point.  The  distance  at  which  the  field  is  taken 
from  day  to  day  should  be  constant.  Fifty  centimeters  is  a  con- 
venient distance  to  employ.  If  the  projection  of  the  lesion  occupies 
five  degrees  of  arc  when  taken  in  the  usual  manner  it  will  appear 
twice  as  big  if  the  eye  is  at  twice  the  distance  from  the  point  of  fix- 
ation. 

The  numbering  of  meridians  has  not  yet  been  universally  agreed 
upon.  Priestly  Smith  and  others  assume  that  the  top  of  the  vertical 
meridian  is  the  starting  point  and  number  in  either  direction  1 80  de- 
grees, denoting  the  temporal  field  as  plus  and  the  nasal  as  negative. 
According  to  Forster  we  should  begin  at  the  left,  and  go  around 
360  degrees,  90  degrees  being  at  the  top.  We  must  always  remem- 
ber that  the  temporal  fields  correspond  to  the  crossed  fibers  in  the 
optic  tracts  and  the  nasal  fields  to  the  uncrossed. 

Measurements  of  the  blind  spot  are  made  by  using  a  small  bright 
test  object.  It  is  increased  in  cases  of  neuritis  and  myopia.  It 
varies  in  size  when  normal  from  4°  to  7°  30'. 

One  of  the  reasons  given  for  the  reduction  of  visual  acuity  outside 
the  macula  lutea  is  that  the  images  falling  upon  the  periphery  of  the 
retina  are  distorted  by  the  rays  of  light  entering  the  eyeball  at  very 
oblique  angles.  Flick  has  shown,  however,  that  the  eye  is  nearly 
periscopic  on  account  of  the  laminated  structure  of  the  crystalline 
lens  neutralizing  this  distortion.     That  the  eye  is  not  exactly  peri- 


154  THE   EYE.    ITS    REFRACTION   AND   DISEASES. 

scopic  may  be  seen  in  emmetropic  eyes,  which  are  hyperopic  in  very 
oblique  axes.  This  is  best  seen  by  performing  retinoscopy  at  a  de- 
cided angle  with  the  visual  axes. 

The  field  of  vision  is  altered  from  a  disturbance  located  anywhere 
in  the  visual  paths.  The  following  divisions  of  the  visual  apparatus 
are  made :  ( i )  The  orbital  portion  (consisting  of  retina,  optic  nerve 
and  chorioid);  (2)  the  optic  nerves;  (3)  the  optic  chiasm;  (4)  the 
optic  tracts  ;  (5)  the  primary  optical  centers  ;  (6)  the  intra-cerebral 
tracts  leading  to  the  cortical  centers  ;  (7)  the  visual  centers  in  the 
cortex  of  the  brain. 

The  manner  in  which  a  diseased  condition  involving  any  of  these 
structures  influences  the  field  of  vision  will  be  considered.  Inasmuch 
as  the  outer  layers  of  the  retina  are  almost  entirely  nourished  by  the 
chorioid  any  disease  in  the  latter  interferes  with  the  welfare  of  the 
former,  as  the  contiguous  layers  of  the  retina  soon  become  involved. 
In  affections  of  the  outer  layers  of  the  retina  scotomata  soon  appear 
in  patches  when  the  nourishment  of  the  delicate  structure  is  altered 
by  a  diseased  process,  while  in  diseases  of  the  inner  layers  of  the 
retina  (hemorrhages,  sclerosis  of  vessels,  degenerations,  etc.)  there  is 
no  characteristic  change  in  the  visual  field,  although  there  is  present 
a  certain  amount  of  amblyopia.  At  the  first  scotomata  can  often  only 
be  outlined  by  aid  of  diminished  light.  In  order  to  render  as  clear  as 
possible  the  symptomatology  of  diseases  of  the  optic  disc  and  inner 
layers  of  the  retina  (nerve  fiber  layers  of  the  retina)  in  contradistinc- 
tion to  that  of  the  outer  retinal  layers  (epithelial  nerve  layers),  as  well 
as  of  the  chorioid  (as  affected  in  chorioido-retinitis)  Wilbrand  com- 
piled the  following  table : 

General  Symptomatology. 
Diseases  of  the  Optic  Nerve,  Optic  Papilla,      Diseases  of  the  Outer  Layers  of  the  Retina 
AND  Innermost  Layers  of  the  Retina.  and  of  the  Chorioid. 

Perception  of  Light. 
Dark   objects   on  a   white  ground         Torpor  retincC 
picked   out    as   well    almost   as    by 
healthy  eye. 


FUNCTIONAL   TESTING.     THE   FIELD    OF   VISION. 


155 


Field  of  Vision  by  Diminished  Light. 


The  eye  acts  as  a  sound  one  and 
shows  the  same  faults  as  by  ordinary 
daylight  illumination. 


By  diminished  light  the  field  of 
vision  shows  either  concentric  con- 
traction zonular  defects,  or  central 
scotomata,  while  by  ordinary  light  no 
defects  can  be  found,  or  the  small  de- 
fects that  are  obtained  are  exagger- 
ated by  diminished  light. 


Forms  of  the  Defects  of  the  Field  of  Vision. 


Large  irregular  defects  with  zones, 
and  islands  (visus  reticulus).  Circular 
scotomata. 


Mostly  concentric  limitation  with 
sector-shaped  reentering  angles.  The 
field  of  color  perception  is  diminished 
as  compared  with  that  for  the  percep- 
tion of  white.  Central  scotomata  with 
diminution  of  the  field  on  one  side  are 

'  Nature  of  Scotomata. 

Central  and  peripheral  negative  sco-  Central  and  peripheral  scotomata 
tomata  which  are  not  recognizable  but  are  positive,  being  recognized  as  dark 
in  which    objects    are    not   ordinarily     spots. 

Central  Visual  Acuity. 
Usually  better   by  diminished  illu-         Usually    less    by    diminished    illu- 
mination.    Nyctalopia.  mination.     Hemeralopia. 


Perception 
Typical  disappearance  of  color  from 
the  field ;  green  goes  first,  then  red 
and  lastly  blue.  Zones  of  dulled  per- 
ception of  color  (color-blindness)  to 
absolute  loss  of  power  of  perception 
of  color.  In  partial  optic  atrophy, 
the  fields  of  white  and  color  approxi- 
mate towards  the  point  of  the  disease. 


of  Color. 

In  ordinary  daylight  concentrically 
limited  field  boundaries.  In  full  light 
the  colors  appear  just  as  they  do  to 
the  normal  eye  by  diminished  light. 
In  the  disturbed  portion  of  the  field 
green  appears  bluish,  yellow  appears 
reddish  and  violet  appears  as  gray. 


Not  present. 


Metamorphopsia  {retinal). 

Commonly  present. 


156  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

The  Field  of  Vision  in  Diseases  Affecting  the  Optic  Nerve. — Both 
inflammatory  and  atrophic  changes  in  the  nerve  give  rise  to  alter- 
ation in  the  field  of  vision.  The  disturbances  in  vision  in  inflamma- 
tory affections  of  the  nerve  are  due  to  destruction  of  conduction 
caused  by  the  swelHng  and  increase  of  the  connective  tissue  septa 
pressing  upon  the  nerve-fibers,  and  partly  by  the  disturbance  in 
nutrition. 

In  simple  optic  atrophy  the  changes  in  vision  are  caused  by  evenly 
spreading  loss  of  power  in  the  individual  nerve  fibers,  of  the  whole 
cross-section  of  the  nerve.  It  is  progressive  and  always  ends  in  blind- 
ness. In  neuritic  atrophy  the  visual  changes  depend  upon  the  dura- 
tion and  intensity  of  the  inflammatory  reaction,  and  the  permanency 
of  the  disturbances  in  nutrition,  to  which  the  individual  bundles  ot 
the  optic  nerve  are  exposed.  In  secondary  descending  atrophy  the 
amount  of  change  is  commensurate  with  the  loss  of  conductivity  of 
the  nerve  fibers  produced  by  disease  of  their  ganglion  cells.  In  dis- 
eases of  the  optic  nerve  and  especially  in  simple  atrophy  the  diminu- 
tion of  the  field  for  white  and  for  color  bear  a  definite  relation  to 
each  other,  which  is  of  the  greatest  importance  for  diagnosis  and 
prognosis.  Defects  first  appear  in  those  portions  of  the  field  whose 
corresponding  retinal  areas  have  in  the  normal  physiological  condi- 
tion the  weaker  visual  acuity.  The  early  defects  are  then  found 
towards  the  periphery  of  the  field. 

If  a  sector-shaped  area  of  the  optic  nerve  is  attacked  more  in- 
tensely, there  will  be  found  a  similar  shaped  defect  projected  into  the 
field  of  white.  The  field  for  blue  will  follow  the  same  conformation. 
If  the  limits  of  the  colored  field  approach  close  to  the  limits  of  the 
white  field  it  proves  that  the  eccentric  acuteness  of  vision  remains 
near  normal.  If  the  defect  divides  both  the  color  and  the  white  fields 
so  that  the  limits  of  the  two  fields  coincide,  we  have  a  condition  known 
as  partial  atrophy,  which  indicates  a  stationary  disease,  and  favorable 
prognosis.  The  relation  of  central  acuteness  of  vision  to  the  defects 
in  the  visual  field  can  not  be  regarded  as  a  constant  one.  Jacobson 
and  Wilbrand  have  arranged  the  following  rules  : 


FUNCTIONAL   TESTING.     THE    FIELD    OF   VISION. 


157 


If  central  vision  falls  off  at  the  same  time  with  eccentric  vision,  it 
is  a  sign  that  the  disease  has  attacked  the  whole  tract.  If  central 
vision  is  diminished  and  the  field  lessened  by  sector-shaped  defects 
which  cut  into  the  field  from  the  periphery,  it  is  a  sign  that  the  whole 
tract  is  affected,  those  parts  related  to  the  sector-shaped  defects  being 
the  more  disturbed.  If  central  vision  is  much  diminished  while  the 
periphery  of  the  visual  field  is  not  much  disturbed,  a  central  scotoma 
relative  or  absolute  is  to  be  thought  of  The  following  is  the  ana- 
tomical condition  of  the  optic  nerves  as  given  by  Henschen. 


Uncrossed  Dorsal 


Uncrossed  Ventral 


The  macular  bundle  lies  ventro-laterally  in  the  papilla  and  also 
immediately  behind  it.  At  the  latter  place  it  forms  a  keystone-shaped 
sector  with  its  base  turned  towards  the  pial  sheath  and  its  apex 
towards  the  central  vessels.     See  figures.     Further  back  this  bundle 


is  half-moon-shaped  ;  still  further  back  it  takes  the  form  of  an  upright 
oval,  and  approaches  nearer  the  axis  of  the  optic  nerve.  In  the  fora- 
men it  assumes  an  axial  position.  In  front  of  the  chiasm  it  assumes 
the  form  of  a  horizontal  oval. 


158 


THE    EYE,    ITS   REFRACTION   AND    DISEASES. 


The  macular  bundle  contains  both  crossed  and  uncrossed  fibers. 
In  the  papilla  the  crossed  fibers  lie  ventrically,  and  the  uncrossed 
ones  more  eccentrically,  being  in  proximity  to  the  other  uncrossed 

fibers.  The  spreading-  of  the  fibers 
over  the  retina  is  as  shown  in  the 
cut  below.  Further  back  the  ma- 
cular bundle  becomes  drawn  to- 
gether towards  the  center,  as  shown 
in  the  second  figure.  The  dorsal 
half  of  these  fibers  goes  to  the  dor- 
sal half  of  the  retina,  and  the  ven- 
tral ones  to  the  ventral  half.  The 
eccentrically  distributed  uncrossed 
bundle  is  divided  in  the  anterior 
division  of  the  optic  nerve  into  two 
fascicles,  a  dorso-lateral  uncrossed 
dorsal  part  and  a  ventro-lateral  uncrossed  ventral  part.  In  the  lam- 
ina cribrosa  these  fibers  are  separated  by  the  macular  bundle.  Be- 
hind the  entrance  of  the  central  vessels  the  fascicles  approach  one 
another  and  form  a  united 
half-moon-shaped  bundle, 
which  includes  the  lateral 
periphery  and  lies  some- 
what ventro-laterally.  The 
crossed  peripheral  distrib- 
uted bundle  forms  a  closed 
cord  in  the  whole  of  the  op- 
tic nerve.  In  the  papilla  it 
is  situated  dorsomesially, 
and  retains  this  position 
until  it  passes  the  chiasm. 

Field  of  Vision  i7i  Diseases  Affecting  the  Chiasm.  —  The  distur- 
bance of  vision  that  is  pathognomonic  of  disturbances  in  conduction 
at  the  chiasm  is  temporal  hemianopsia  in  its  various  manifestations. 


L.E. 


R.E. 


s;o' 


FUNCTIONAL   TESTING.     THE   FIELD    OF   VISION.  159 

It  is  observed  only  in  organic  lesions  and  does  not  occur  as  a  func- 
tional disease.  By  hemianopsia  (hemiablepsia)  is  meant,  complete 
or  partial  loss  of  sight  affecting  one  half  of  the  field  of  vision. 

The  term  temporal  or  nasal  hemianopsia  has  to  do  with  the  portion 
of  the  field  affected  and  not  with  the  portion  of  retina  involved,  thus 
temporal  hemianopsia  means  loss  of  sight  in  the  temporal' field. 
The  eye  affected  with  hemianopsia  is  said  to  be  hemianoptic 
(hemiopic).""'' 

The  figure  above  represents  the  hemianoptic  fields,  with  the  sco- 
tomata  reaching  up  to  and  involving  half  of  the  fixation  point.  At 
times  the  line  of  separation 
between  the  halves  of  the 
field  of  vision  in  temporal 
hemianopsia  does  not  always 
lie  vertically  and  may  be  situ- 
ated beyond  the  point  of  fix- 
ation, forming  the  so-called 
overshot  field  of  vision.  The 
latter  could  only  occur  in  cases 
in  which  the  maculae  were  provided  with  a  double  set  of  nerves,  one 
set  from  each  hemisphere.  The  arrangement  of  the  optic  fibers  in 
the  chiasm  is  shown  in  the  figure. 

Pressure  from  an  exudate  or  tumor  involving  the  upper  or  lower 
half  of  the  chiasm  may  give  rise  to  a  binocular  inferior  or  superior 
hemianopsia. 

The  Field  of  Vision  in  Diseases  of  the  Optic  Tracts. — The  pathog- 
nomonic disturbance  in  the  visual  field  in  diseases  involving  the 
tracts  is  homonymous  hemianopsia,  also  called  lateral  hemianopsia. 
In  this  condition  the  left  or  the  right  field  in  each  eye  is  destroyed. 
There  is  some  difference  in  regard  to  the  line  of  separation  of  the 
two  portions  of  the  field  in  different  cases.  In  some  the  line  of  sep- 
aration cuts  through  the  point  of  fixation.     In  another  type  the  line 

*  The  terms  hemiopia  and  hemianopsia  are  often  used  synonymously,  but  really  hemiopia  signifies 
loss  of  perceptive  power  of  one  half  of  the  retina,  while  hemianopsia  means  obscuration  of  one  half  of 
the  visual  field. 


i6o 


THE   EYE,    ITS    REFRACTION   AND    DISEASES 


of  separation  is  carried  past  the  fixation  point  to  the  advantage  of 
the  remaining  halves  of  the  field  of  vision.  Lateral  hemianopsia  is 
caused  by  organic  diseases  only  and  is  absolute,  that  is  within  the 
blind  portions  of  the  fields  nothing  at  all  is  seen.  The  hemianoptic 
fields  may  be  incomplete,  that  is  a  scotoma  may  occupy  the  corre- 
sponding part  of  the  field  of  each  eye. 


LEFT    HOMONYMOUS     HEMIANOPSIA    CAUSED    BY    INVOLVEMENT     OF     THE 

RIGHT   OPTIC   TRACT. 

Hemianopsia  in  Lesions  of  the  PriTnary  Optical  Centers. — By  the 
primary  optical  centers  is  meant  the  corpus  geniculatum,  the  corpus 
quadrigeminum,  and  the  optic  thalamus.  A  diseased  focus  affecting 
the  primary  optic  centers  gives  rise  to  homonymous  hemianopsia, 
and  hemiplegia  and  hemiaesthesia  of  the  same  side  from  common  in- 
volvement of  the  neighboring  fibers  that  pass  through  the  internal 
capsule  of  the  pedunculus  cerebri.  If  the  posterior  end  of  the  tract 
is  involved  the  hemianoptic  pupillary  reaction  is  observed. 

If  the  lesion  is  placed  more  centrally,  that  is  posterior  to  the  thala- 
mus, the  pupils  will  react  when  the  light  is  thrown  upon  the  blind 
half  of  either  retina,  and  there  is  homonymous  hemianopsia  perhaps 
only  for  colors,  or  there  is  complete  blindness.  In  some  cases  cen- 
tral vision  is  retained  if  the  maculae  have  a  double  innervation. 


CHAPTER   X 

THE    COLOR-SENSE 

The  ability  of  the  eye  to  discern  different  colors  is  called  the  color 
sense.  As  has  been  seen,  a  ray  of  white  light  when  passed  through 
a  prism  is  broken  up  into  spectral  colors  :  red,  orange,  yellow,  green, 
blue,  indigo  (?)  and  violet.  These  colors  are  called  simple  colors 
because  they  cannot  be  further  divided.  They  likewise  compose  the 
visible  spectrum,  the  part  of  the  entire  spectrum  that  can  be  per- 
ceived by  the  unaided  eye.  Objectively  the  various  colors  consist 
of  rapid  vibrations  of  the  ether,  from  about  400  millions  of  millions 
per  second  for  red,  to  about  760  millions  of  millions  per  second  for 
violet.  At  each  end  of  the  visible  spectrum  there  are  waves  pro- 
ceeding of  such  a  refrangibility  that  the  colors  are  not  perceived  by 
the  eye.  These  are  the  ultra-red  and  ultra-violet  rays.  The  reason 
given  for  their  invisibility  is  that  the  waves  are  of  such  a  length  that 
they  are  absorbed  by  the  media  of  the  eye,  and  therefore  never  reach 
the  retina  to  stimulate  it.* 

The  ultra-violet  rays  can  be  perceived  by  receiving  them  upon  a 
photographer's  plate,  or  upon  a  fluorescent  screen,  or  by  eliminating 
all  other  light  by  painting  the  screen  with  a  fluorescent  substance,  as 
sulphate  of  quinine  or  fluorescein.  These  substances  struck  by  the 
ultra-violet  rays  send  back  visible  rays  usually  bluish  or  greenish. 
With  the  proper  precautions  the  ultra-violet  rays  may  be  seen  of  a 
grayish  color,  perhaps  as  the  retina  is  itself  fluorescent.  It  is  the 
ultra-violet  rays  that  are  abundant  in  winter  and  in  high  altitudes 
that  are  supposed  to  be  the  cause  of  snow-bhndness.  It  is  possible 
to  mix  or  blend  color  sensations  in  the  eye  by  stimulating  the  same 
area  of  the  retina  by  different  colors  at  the  same  time  or  in  rapid 

*  Only  those  waves  whose  wave-length  is  between  .00036  and  .00075  can  be  seen. 

161 


1 62 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


succession.     The  following  table  shows  the  results  of  such  experi- 
ments performed  by  Von  Helmholtz  : 


j        Violet. 

Indigo 

Cyan-blue. 

Blue  Green. 

Green. 

Green  Yellow.   Yellow. 

Red. 

Purple. 

Dark  rose. 

White  rose. 

White. 

^Vhite  yellow. 

Gold  yellow. 

Orange, 

Orange, 

Dark  rose. 

White  rose. 

White. 

White  yellow. 

Yellow. 

Yellow. 

Yellow. 

White  rose. 

White. 

White  green. 

White  yellow. 

Green  yellow. 

Green  blue. 

White. 

White  green. 

White  green. 

Green. 

Green. 

White  blue. 

Water  green. 

Bluish  green. 

. 

Bluish  green. 

Water  blue. 

Water  blue. 

Cyan-blue. 

Indigo. 

These  are  mixed  colors.  As  will  be  seen  only  two  new  colors  can 
be  produced,  namely  :  white  and  purple,  the  other  mixed  colors  hav- 
ing their  equivalent  in  the  spectrum.  White  and  purple  have  no 
objective  equivalent  in  a  simple  number  of  ether  vibrations.  Any 
two  colors  that  produce  white  when  mixed  together  are  called 
complementary  colors.  Such  are  red  and  green-blue,  golden  yellow 
and  blue,  green  and  purple.  The  mixture  of  all  the  spectral  colors 
of  course  produces  white.  Different  results  are  obtained  by  mixing 
colored  pigments,  however.  On  the  painter's  palette  yellow  and  blue 
produce  green,  but  in  the  eye  white.  The  reason  for  this  is  that  the 
colors  of  nature  are  mixtures  of  simple  colors,  as  can  be  seen  by 
spectroscopic  analysis,  or  by  mixing  spectral  colors.  There  are  three 
primary  qualities  resident  in  all  colors :  hue  (ton),  purity  or  tint 
(saturation),  and  brightness  or  luminosity  (intensite).  The  first  gives 
the  name  to  the  color,  red,  blue  or  what  not.  The  second  depends 
upon  the  admixture  of  white  in  all  colors,  save  those  of  the  spec- 
trum. The  third  quality  depends  upon  the  objective  intensity  of  the 
light  and  the  sensibility  of  the  observer's  retina.  As  pointed  out  on 
a  preceding  page  the  ability  to  see  the  different  colors  diminishes 
towards  the  periphery  of  the  retina,  blue  being  seen  the  furthest 
from  the  center. 

Theories  of  Color  Perception. — The  theory  of  Helmholtz  origi- 
nated by  Thomas  Young,  assumes  that  there  is  in  the  retina  three 
different  kinds  of  end-organs,  each  of  which  is  loaded  with  its  own 


THE   COLOR-SENSE.  1 63 

photo-chemical  substance,  which  is  decomposed  by  a  certain  number 
of  ether  vibrations  and  thus  excites  the  optic  nerve. 

One  group  is  loaded  with  a  red  sensitive  substance,  and  is  affected 
mainly  by  the  red  end  of  the  spectrum;  another  group  of  end-organs 
is  loaded  with  a  green  sensitive  substance,  and  answers  to  the  green 
portion  of  the  spectrum,  while  the  third  group  is  provided  with  a 
blue  sensitive  substance,  chiefly  decomposed  by  the  blue-violet  end 
of  the  spectrum. 

All  three  end-organs  are  present  in  different  parts  of  the  retina, 
and  are  connected  by  special  nerve  fibers  with  special  parts  of  the 
brain,  in  the  cells  of  which  is  stored  the  memory  of  the  sensation  of 
red,  green  or  blue.  All  other  color  sensations  arise  from  these  pri- 
mary sensations.  If  a  color  rnainly  excites  the  red  or  green  sub- 
stance, we  term  it  red  or  green  respectively.  The  equal  and  simul- 
taneous stimulation  of  the  red  and  green  carrying  end-organs  gives 
rise  to  a  sensation  of  yellow,  that  of  red  and  blue  to  the  sensation 
of  purple,  and  that  of  blue  and  green  to  that  of  blue-green.  The 
simultaneous  stimulation  of  all  three  substances  of  a  certain  area  to 
the  same  degree  gives  the  impression  of  white.  Complementary 
colors,  according  to  this  theory,  are  those  that  excite  all  three  color- 
substances  at  the  same  time  and  to  the  same  degree.  Color-blind- 
ness is  supposed  to  be  caused  by  two  of  the  color-substances  being 
or  becoming  similar,  or  equal  to  each  other  or  that  one  or  more  of 
them  is  absent.  Thomas  Young  supposed  that  each  spectral  color 
stimulated  one  or  perhaps  two  of  the  color  end-organs  in  varying 
degrees,  while  Helmholtz  supposed  that  all  spectral  colors  stimulated 
all  three  end-organs  at  once,  but  to  different  degrees. 

The  theory  of  Hering  was  developed  about  four  years  later,  in 
1874.  It  assumes  that  the  process  of  restitution  in  a  nerve  element 
is  capable  of  exciting  a  sensadon.  There  are  accordingly  three 
visual  substances  in  the  retina,  namely :  a  white-black,  a  red-green 
and  a  yellow-blue  visual  substance.  A  destructive  process  in  the 
white-black  substance,  not  only  occasioned  by  white  light,  but  as  well 
by  any  simple  or   mixed  color,   produces   the   sensation  of  white, 


l64  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

while  the  process  of  assimilation  or  restitution,  gives  the  sensation  of 
black. 

Red  light  similarly  produces  a  destruction  in  the  red-green  sub- 
stance and  the  sensation  of  red  while  its  reconstruction  by  a  green 
light  causes  the  sensation  of  green.  The  sensation  of  yellow  has  its 
cause  in  the  decomposition  of  the  yellow-blue  substance  by  yellow 
light,  while  blue  light  causes  a  reconstruction  and  the  sensation  of 
blue.  Simultaneous  processes  of  dissimilation  and  assimilation  in 
the  same  substance  antagonize  each  other  and  cause  the  sensation 
of  no  color,  white  being  the  result,  by  decomposition  of  the  white- 
black  substance.  Color  blindness  is  explained  by  this  theory  by  as- 
suming that  either  the  red-green  or  the  yellow-blue  substance  in  the 
retina  is  absent. 

Among  the  more  recent  theories  of  color  perception  may  be  men- 
tioned that  of  Ebblnghaus,  who  supposes  that  there  exists  in  the 
cones  a  green  substance,  the  decomposition  of  which  would  produce 
the  sensation  of  red  and  green,  while  the  visual  purple  by  its  decom- 
position would  produce  the  sensation  of  yellow  and  blue.  Perinaud 
supposes  that  the  stimulation  of  the  rods  produces  a  sensation  of 
non-colored  light,  while  stimulation  of  the  cones  produces  all  possi- 
ble sensations,  the  sensation  of  white  and  that  of  color.  The  retina 
would  then  have  two  systems  sensitive  to  light,  one  monochromatic 
and  the  other  trichromatic.  Von  Kries  agrees  with  the  views  of 
Perinaud.  Arthur  Konig  believes  that  the  decomposition  of  the 
retinal  purple  into  yellow  produces  a  weak  sensation  of  gray,  which 
causes  any  color  when  it  is  sufficiently  weak. 

Further  decomposition  produces  the  sensation  of  blue.  The  per- 
ception of  the  two  other  principal  colors,  namely  green  and  red,  is 
affected  through  the  pigment  cells,  while  the  cones  are  considered  to 
be  dioptric  agents  intended  to  concentrate  the  light  upon  the  epi- 
thelial layer  of  the  retina. 

H.  Muller  measured  the  distance  of  the  retinal  vessels  from  the 
sensitive  layer  of  the  retina  by  means  of  the  parallax  of  the  vessels 
seen  entoptically.     In  collaboration  with  Zumft  he  made  these  experi- 


r 


THE   COLOR-SENSE.  igr 

ments  with  spectral  light.  He  found  that  the  distance  gradually  in- 
creased as  he  approached  towards  the  red  end  of  the  spectrum.  The 
layer  sensitive  to  red  light  would  then  be  posterior,  to  that  sensitive 
to  blue.  These  experiments  have  been  repeated  by  others  without 
success. 

Congenital  color-blindness  is  called  daltonism  (achromatopsia)  from 
the  English  physicist  (Dal ton)  who  first  described  the  anomaly,  he 
being  himself  color-bHnd.  There  is  a  form  of  acquired  color-blind- 
ness due  to  poisoning  by  tobacco  and  alcohol.  The  commonest  form 
of  daltonism  is  red-blindness ;  according  to  the  Hering  theory,  red- 
green-blindness.  It  occurs  oftener  in  males  than  in  females,  about 
three  to  four  per  cent,  of  the  former  being  affected.  Perhaps  women 
are  less  often  color-bHnd  from  undergoing  a  sort  of  training  in  busy- 
ing themselves  with  colors,  as  in  making  dresses,  fancy  articles  and 
so  on — the  taste  for  these  things  being  inherited. 

Color-blindness  does  not  cause  any  inconvenience  to  its  possessor 
further  than  that  it  unfits  him  for  certain  callings  in  life,  as  that  of  a 
painter,  dyer,  tailor  or  for  the  railroad  or  marine  service.  Those  em- 
ployed in  railroad  or  marine  service  should  have  a  good  color  sense 
as  the  signals  used  in  each  are  the  colors  that  are  most  apt  to  be 
confounded  by  the  color-blind  ;  they  are  red  and  green.  Employees 
should  also  be  tested  once  a  year  for  acquired  color-blindness,  if  they 
are  users  of  alcohol  or  tobacco.  The  next  most  frequent  form  of 
congenital  color-blindness  is  yellow-blue-blindness,  also  called  violet- 
blindness. 

It  seems  strange  that  the  two  colors  which  are  most  often  confused 
should  be  used  in  a  service  where  the  Hves  of  hundreds  of  people 
are  concerned.  The  colors  in  use  are,  however,  those  that  have  the 
highest  degree  of  luminosity,  and,  therefore,  can  be  seen  at  the 
greatest  distance  off.  White  light,  having  the  greatest  penetrability, 
is  Hkewise  used  for  signaling.  A  white  light  seen  through  a  bank 
of  haze  or  fog  often  appears  red,  as  the  red  rays  have  the  longest 
wave-length  of  the  spectrum  and  are,  therefore,  best  able  to  pene- 
trate the  obstruction  offered  by  the  foggy  medium.     They  are  most 


1 66  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

conspicuous  at  the  end  of  their  journey.  In  the  neighborhood  of 
large  towns  and  cities  the  sun  almost  always  sets  as  a  red  ball  of 
fire,  as  above  them  usually  floats  a  bank  of  haze.  As  the  sun  sinks 
to  rest,  the  green  rays  are  first  absorbed,  then  the  yellow  and  lastly 
the  orange  and  the  red,  the  latter  often  the  only  one  to  get  through. 
(The  blue  of  the  vault  of  the  heavens  is  said  to  be  due  to  the  reflec- 
tion and  scattering  of  the  blue  rays  of  light  by  the  myriads  of  atoms 
of  dust  that  pervade  all  space.  The  blue  rays,  having  a  short  wave- 
length, are  unable  to  pass  through).  A  person  born  blind  to  certain 
colors  can  often  name  properly  one  of  those  colors  when  it  is  pre- 
sented to  him.  To  him  colors  are  recognized  simply  by  their  lumi- 
nosity or  valence  (intensite).  Since  early  childhood  the  color-blind 
individual  has  been  hearing  people  say  that  leaves  of  trees  are  green 
and  that  cherries  are  red  and  so  on.  The  association  of  the  color 
and  the  object  is  mentally  fixed  and  every  time  in  adult  life  that  he 
sees  a  cherry  he  thinks  of  red  and  looking  at  the  trees  and  grass  he 
calls  them  green.  He  is  apt  to  become  confused,  however,  if  red 
and  green  differing  from  the  shades  found  in  nature  be  given  him. 
To  the  absolutely  color-blind  a  landscape  looks  like  an  etching, 
made  of  varying  shades  of  gray.  Or,  if  blind  only  for  certain  colors, 
those  colors  will  be  wanting  in  his  conception  of  th^  picture,  each 
being  replaced  by  a  gray  of  the  same  intensite  as  the  color  itself 
The  color-blind  engineer  may  get  along  all  right  in  clear  weather, 
when  there  is  no  fog  or  mist,  and  be  able  to  keep  separate  in  his 
mind  the  difference  between  the  red  and  green  signal  lights.  But, 
if  a  fog  comes  up  to  obscure  the  signal  somewhat,  then  the  lumi- 
nosity of  the  light  being  altered,  he  has  nothing  by  which  to  judge  of 
the  color,  and  an  accident  happens  through  the  failure  on  the  part 
of  the  engineer  to  appreciate  the  difference  between  red  and  green 
lights.  The  demonstration  of  color-blindness  requires  accurate  and 
painstaking  testing.  Many  of  those  who  are  aware  of  their  defect 
try  to  conceal  it  from  the  examiner,  especially  if  a  good  position  is 
dependent  upon  a  normal  color  sense.  We  must  look  out  then  for  all 
sorts  of  tricks,  when  testing  men  for  the  railroad  or  marine  service. 


THE   COLOR-SENSE.  1 67 

Frequently  by  practice  the  man  has  made  himself  adept  in  the 
methods  of  testing  commonly  used  for  the  detection  of  color-blind- 
ness. On  the  other  hand,  persons  with  poor  color  appreciation 
(dyschromatopsia)  and  education  may  be  considered  color-blind  if 
they  are  simply  asked  to  name  colors  placed  before  them.  We 
never  test  the  color  sense  by  setting  different  colors  before  the  patient 
and  ask  him  to  name  them,  for  the  color-blind  individual  will  often 
by  a  little  attention  give  the  right  answer  and  the  uneducated  will 
just  as  often  give  the  wrong  answer.  The  test  is  best  conducted  by 
setting  before  the  patient  those  colors  which  experience  has  shown 
are  most  apt  to  be  confused,  and  then  a  large  collection  of  colored 
worsteds  are  given  him  from  which  he  is  to  select  those  skeins  that 
match  the  confusion  color.  If  then  colors  quite  dissimilar  are  placed 
together,  for  instance  gray,  red  and  green,  color-blindness  exists.  It 
is  possible  to  tell  what  kind  of  color-blindness  the  individual  has 
according  to  the  colors  he  confuses.  Thus,  if  a  red  skein  is  given 
him  to  match  and  he  places  besides  it  other  colors  of  the  same  shade, 
it  is  evident  that  he  is  blind  to  red,  and  if  he  fails  properly  to  match 
the  green  he  is  blind  to  green  and  so  on.  This  test  is  the  Seebeck 
or  Holmo-ren  test. 

The  next  most  commonly  employed  test  is  that  with  the  pseudo- 
isochromatic  diagrams  of  Stilling.  These  consist  of  squares  composed 
of  different  colors,  so  arranged  that  they  form  figures  or  letters. 
The  colors  of  the  test  have  been  selected  by  a  color-blind  painter  so 
that  they  will  correspond  to  the  confusion  colors  of  the  color-blind. 

To  the  latter  then  all  the  squares  appear  to  be  of  the  same  shade 
and  the  letters  or  figures  are  not  seen.  The  spectroscope  is  indis- 
pensable for  the  scientific  estimation  of  color-blindness.  We  can 
find  out  what  colors  in  the  spectrum  are  missing  and  by  showing  the 
patient  an  isolated  portion  of  the  spectrum  make  him  tell  both  by 
naming  and  by  matching  the  color  how  the  spectrum  looks  to  him. 
For  the  quantitative  color  sense,  the  tests  of  Donders,  Weber  and 
Wollfberg  are  used.  Small  discs  of  colored  paper  upon  a  back- 
ground of  black  satin  serve  for  test  objects. 


1 68 


THE   EYE.    ITS   REFRACTION   AND   DISEASES. 


If  the  color  sense  is  normal  colored  discs  of  different  sizes  must 
be  recognized  at  given  distances.  The  distance  at  which  the  disc  is 
discernible  varies  for  different  colors.     The  stronger  the  color  sense 

Dr.  Williams'  Lantern  for  Testing  the  Color  Sense  of  Employees  in  the  Railway  or 
Marine  Service  who  use  Colored  Signals  by  Night. 
On   the   front  of  this 

lantern  are  two  movable 

discs,  the  lower  has  five 

green  and  five  red  glasses 

of  different   shades,   one 

yellow,  one  blue  and  one 

white  glass.     The  upper 

disc  has   London  smoke 

glass    of    three   different 

shades   and    some    clear 

openings.      By     rotating 

the    discs   by    hand    any 

of    the     colors    can     be 

shown,  either  alone  or  in 

combination      with      the 

smoke    glass.       Between 

the  discs  is  a  movable  di- 
aphragm which  regulates 

the    size    of  the   colored 

area  shown.     Inside  the 

lantern  are  two  pieces  of 

ground   glass  which  can 

be  placed  before  the  light 

when  desired,  giving  the 

effect  of  fog.     The  lamp 

is  arranged  with  two  sep- 
arate burners,  and  by  having  two  openings  in  the  front  of  the  lantern  it  is  possible  to  show  two  colors 
at  the  same  time  in  contrast,  or  by  moving  the  diaphragm  to  have  only  one  color  shown.  In  this  way 
red  and  green,  two  reds  or  two  greens  of  different  shades,  red  and  white,  etc.,  can  be  shown  at  the 
same  time,  or  any  one  color  can  be  shown  by  itself.  In  connection  with  each  glass  there  is  an  illumi- 
nated number  or  letter  which  can  be  seen  by  the  person  making  the  examination,  but  which  is  screened 
from  the  person  tested.  By  this  means  a  record  can  be  kept  of  the  color  shown,  and  the  name  given  to 
it.  This  lantern  makes  a  very  useful  addition  to  the  Worsted  Test  and  will  detect  some  cases  of  defec- 
tive color  perception,  especially  where  it  is  confined  to  a  small  central  area  in  the  retina,  which  are  not 
discovered  by  the  Worsted  Test. 

of  the  individual  the  further  can  he  recognize  the  given  color  and 
vice  versa.  The  intensity  of  the  color  sense  for  the  color  in  question 
is  the  distance  at  which  it  begins  to  be  recognized.     Dr.  Oliver  has 


THE   COLOR-SENSE.  1 69 

devised  a  convenient  apparatus  for  measuring  the  color  sense  at  a 
given  distance.  He  found  that  red  requires  2.65  mm.  of  square 
surface  to  be  recognized  at  a  distance  of  5  m.;  yellow  a  slightly- 
larger  area,  and  violet  22.75  ^^-  of  square  surface.  Instead  of 
colored  papers  we  may  use  colored  lights,  and  thus  more  closely 
approximate  the  conditions  present  in  railroad  and  marine  service. 
These  tests  are  called  lantern  tests.  The  lantern  shown  in  the  cut 
above  is  a  sample  and  probably  the  best  lantern  on  the  market  for 
testing  the  color  sense  of  employees  in  railroad  and  marine  service. 

One  other  test  will  be  mentioned,  that  of  Meyer.  If  a  border  of 
gray  paper  is  placed  upon  red  paper,  it  appears  to  have  the  comple- 
mentary color,  that  is  green.  This  is  especially  the  case  when  the 
whole  is  covered  with  a  piece  of  tissue  paper.  A  color-blind  person 
who  does  not  recognize  the  color  of  the  background  fails  to  tell  the 
color  of  the  border  as  well.  Daltonism  (dichromasia)  is  incurable. 
Acquired  color-blindness  is  caused  by  affections  of  the  light-perceiv- 
ing apparatus. 

There  seems  to  be  a  special  color  center  in  the  occipital  cortex, 
and  affections  of  this  as  well  as  affections  of  the  optic  tract,  nerve  or 
retina  destroy  the  appreciation  of  color,  leaving  the  form  or  space 
sense  intact.  There  is  evidence  that  this  color  center  is  capable  of 
perceiving  six  separate  and  independent  colors.  There  is  a  tendency 
of  late  to  accept  this  central  color-sense  theory  to  the  exclusion  of 
the  retinal  theories. 

Diseases  of  the  optic  nerve  are  the  most  frequent  causes  of  ac- 
quired color-blindness.  Such  is  never  absent  when  the  vision  is 
much  reduced.  The  loss  of  the  color  sense  sets  in  gradually  and 
not  for  all  the  colors  at  once.  First  of  all  the  perception  of  green 
and  red  is  extinguished,  then  that  for  yellow,  and  lasdy  that  for  blue. 
That  color  for  which  the  least  extent  of  the  retina  is  sensitive  disap- 
pears first  and  that  for  which  most  of  the  retina  is  sensitive  persists 
the  longest.  The  perception  of  color  remains  intact  when  the  vision 
is  reduced  from  other  causes  than  implication  of  the  light-perceiving 
apparatus. 


170  THE   EYE,    ITS   REFRACTION    AND    DISEASES. 

No  definite  results  can  be  obtained  in  infants  under  six  months  of 
age  as  to  the  condition  of  color  perception.  After  this  age  there  is 
usually  a  reaction  obtained  for  red,  orange  and  yellow,  that  is  the 
infant  will  reach  after  and  seem  pleased  at  the  sight  of  ribbons  of 
these  colors.  Between  the  ages  of  ten  and  twelve  months  there  is 
an  equal  reaction  for  all  colors.  Tests  for  color  preference  show 
preference  for  red  between  the  seventh  and  the  twenty-fourth  month. 
Blue  preference  begins  in  33  per  cent,  between  the  ages  of  two  and 
three  years,  and  increases  to  93  per  cent,  in  the  thirteenth  year.  A 
typical  choice  without  preference  begins  with  44  per  cent,  between 
the  ages  of  three  and  four  years  and  decreases  to  7  per  cent,  at  the 
thirteenth  year. 


CHAPTER   XI 

THE    LIGHT    SENSE 

Two  persons  that  have  the  same  visual  acuity  in  good  illumination 
are  often  not  able  to  read  equally  well  when  the  illumination  is  re- 
duced. These  two  people  have  the  same  space  sense,  but  their 
retinae  are  differently  affected  by  brightness  or  difference  of  illumina- 
tion. The  one  who  can  read  the  better  when  the  light  is  reduced 
has  the  better  light  sense. 

The  light  sense  is  tested  in  several  ways.  We  can  determine  the 
smallest  amount  of  illumination  by  which  an  object  can  be  seen 
(minimum  stimulus)  or  the  smallest  difference  of  brightness  that  can 
be  appreciated  (minimum  of  difference).  In  practice  when  we  only 
wish  to  know  whether  the  light  sense  is  reduced  or  not,  as  patients 
with  certain  eye  diseases  see  better  in  feeble  illumination,  while 
others  read  better  in  a  bright  light,  we  can  gradually  lessen  the 
amount  of  light  that  falls  upon  the  test  card,  and  note  whether  the 
patient  sees  poorer  in  proportion  as  the  light  is  reduced  than  we  do, 
that  is  whether  his  vision  falls  off  faster  than  ours.  The  light-sense 
is  not  always  diminished  when  the  vision  is  disturbed,  but  the  vision 
may  be  very  poor  and  the  light  sense  very  good  and  vice  versa. 
When  a  patient  sees  better  by  day  or  by  a  bright  light,  he  has  what 
is  termed  hemeralopia,  and  when  he  sees  better  when  the  illumina- 
tion is  feeble,  we  call  it  nyctalopia.  These  two  terms  are  often  con- 
fused, the  latter  being  at  times  used  to  indicate  night-blindness. 
The  first  term,  hemeralopia,  is  derived  from  the  two  Greek  words : 
i7/xe/3a.  day,  and  (m/zt?,  sight,  that  is  day  sight.  The  etymology  of  the 
latter  term,  nyctalopia,  is  :  wt  night,  an/;t9,  sight,  that  is  night  sight. 

The  scientific  method  of  testing  the  light  sense  is  with  one  of  the 
various  photometers,  which  gives  the  minimum  stimulus.  The  in- 
strument usually  employed  is  that  of  Forster.     It  consists  of  a  box, 

171 


172  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

light-tight  and  blackened  on  the  inside.  In  one  corner  of  the  box 
there  is  a  normal  candle  —  one  burning  i20grs.  in  one  hour  —  made 
of  spermaceti.     The  candle  illumines  the  interior  of  the  box  through 

the  window  W,  the  size  of  which  can 
be  altered  by  means  of  the  screw  S. 
The  window  is  covered  with  oiled  paper 
so  that  the  light  emitted  will  be  per- 
fectly uniform.  Upon  the  opposite  side 
FORSTER's  PHOTOMETER.  ^f  the   interior  of  the  box   is  hung  a 

card    made    of  alternating   black    and 
white  stripes,  to  be  used  as  the  test  object. 

The  patient  after  remaining  in  the  dark  for  a  while,  in  order  that 
his  eyes  may  become  adapted  to  the  darkness,  looks  into  the  appa- 
ratus with  the  window  W  closed,  and  the  test  card  unillumined  in 
consequence.  Then  the  light  is  allowed  to  enter  the  box  slowly 
through  the  window,  until  the  stripes  upon  the  card  can  be  seen. 
The  size  of  the  opening  needed  for  this  purpose  is  a  measure  of  the 
light  sense  of  the  individual  under  examination. 

One  day  Fechner  noticed  a  scarcely  perceptible  difference  between 
the  brightness  of  two  clouds,  and  that  this  difference  persisted  on  look- 
ing through  a  smoked  glass.  This  observation  caused  him  to  formulate 
the  following  law  :  The  smallest  difference  of  perceptible  illumination 
is  a  constant  fraction  (about  one  per  cent.)  of  the  total  illumination. 
This  is  a  general  law  of  perception  as  it  applies  to  the  other  senses. 
If  a  string  must  have  a  length  of  105  mm.  before  we  can  tell  by  ob- 
servation that  it  is  longer  than  one  that  has  a  length  of  100  mm.,  we 
find  that  another  must  be  at  least  210  mm.  in  lenofth  before  we  can 
tell  that  it  is  longer  than  one  of  200  mm.  This  proportion  holds  no 
matter  how  long  the  string  is.  It  is  also  with  sound  and  the  estimate 
of  the  difference  between  two  weights.  Bouguer  observed  the  fact 
upon  which  Fechner  based  his  law  some  time  previously.  He  also 
described  the  following  experiment  to  determine  the  ratio  between 
the  smallest  difference  of  perceptible  illumination  and  the  total  illu- 
mination. 


THE    LIGHT-SENSE. 


n?> 


A  and  B  are  two  lights  placed  at  different  distances  in  front  of 
screen  SS'.  6>  is  a  stick  so  placed  that  it  casts  two  shadows  upon 
SS'\  a  from  A,  and  b  from  B.  The  shadow  b  is  illuminated  ?nd 
thus  rendered  fainter  by 
A,  as  is  a  by  B.  By  mov- 
ing the  light  B  further 
away  the  shadow  b  be- 
comes feebler  and  at  last 
disappears  when  the  light 
B  is  ten  times  further  from 
the  screen  than  A.  The 
same  thing  occurs  with 
lights  of  different  intensi- 
ties, that  the  moment  when 
the  shadow  of  one  fades  away,  that  light  is  ten  times  further  off 
than  the  other  one.  The  amount  of  illumination  is  proportional 
to  the  intensity  of  the  luminous  source,  and  inversely  proportional  to 
the  square  of  the  distance.  Suppose  that  B  is  200  cm.  from  the 
screen,  and  A  at  20  cm.  and  /  their  intensity.  A  gives  to  the  screen 
a  lumination  of  1/20^  and  B  of  1/200^,  and  the  shadow  b  receives 
1/20^  illumination.  The  difference  between  the  illumination  of  the 
shadow  and  the  screen  is 


( I  /  20^  +  I  /  200^^)  —  I  /  20^  =  I  /  200^. 

(The  intensity  of  light  varies  inversely  as  the  square  of  the  distance.) 
The  ratio  between  this  difference  and  the  illumination  of  the  screen  is 


/ 


200^ 


lOI 


or    1 1  loo; 


since  the  measurements  were  purposely  taken  in  round  numbers  to 
simplify  the  problerri,  but  are  not  very  exact. 


174  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

If  the  intensity  of  the  lights  is  doubled,  then  : 

2/ 


200^ 

I 

2/     2/ 

lOI 

Many  phenomena  daily  observed  are  explained  by  the  law  of  Fech' 
ner.  We  read  by  artificial  light  as  well  as  we  do  by  daylight,  although 
the  illumination  in  the  daytime  is  enormously  greater  than  by  gas- 
light, because  the  light  reflected  by  the  white  paper  and  the  black 
letters  remains  the  same.  This  law  is  only  true  for  medium  degrees 
of  illumination.  If  the  illumination  is  very  feeble  the  relative  differ- 
ence must  be  much  more.  If  the  gaslight  is  much  lowered,  we  can 
not  see  any  longer  to  read,  although  the  illumination  of  the  print  and 
the  paper  bears  the  same  ratio.  It  is  possible  that  this  difference  is 
due  to  what  is  called  the  retina's  own  light,  designating  the  feeble 
glow  which  may  be  perceived  in  a  dark  room,  which  is  due  to  internal 
causes,  perhaps  the  friction  of  the  blood  in  the  vessels  against  the 
sensitive  layer  of  the  retina,  and  perhaps  also  certain  processes  in  the 
brain.  If  this  light  is  added  to  that  of  the  printed  sheet,  the  differ- 
ence of  brightness  between  the  letters  and  the  papepmay  fall  below 
the  limit  of  Fechner.  The  law  also  ceases  to  act  when  the  light  is 
very  strong  —  the  reason  why  we  cannot  see  the  sun's  spots  with 
the  naked  eye  on  account  of  dazzling,  but  very  well  with  a  smoked 
glass. 

The  illumination  of  a  fair  day  is  the  most  favorable  amount  of  light 
to  verify  Fechner' s  Law.  The  acuity  of  the  light-sense  is  expressed 
by  the  inverse  of  the  fraction  of  Fechner.  If  it  be  one  one-hundredth 
then  the  luminous  sense  is  100,  and  if  by  greatly  diminishing  the  illu- 
mination the  fraction  rises  to  one  fiftieth,  we  say  that  the  acuity  is  50 
and  so  on. 

The  degree  of  illumination  that  forms  the  lowest  limit  of  visibility 
is  called  the  threshold.  According  to  Aubert,  the  weakest  light  that 
the  eye  can  distinguish,  or  the  threshold  of  the  normal  eye,  is  a  sheet 


THE    LIGHT-SENSE. 


175 


of  white  paper  illumined  by  a  candle  placed  at  a  distance  of  200-250 
m.  For  very  feeble  illumination  the  macula  lutea  is  less  sensitive 
than  the  parts  of  the  retina  that  immediately  surround  it.  By  fixing 
a  point  a  little  to  one  side  of  the  macula,  we  better  distinguish  the 
brightness,  which  differs  only  slightly  from  that  of  the  background, 
as  when  we  try  to  see  very  dim  stars,  for  example.  Parinaud  says 
that  this  is  because  the  macula  is  not  able  to  adapt  itself  like  the  rest 
of  the  retina,  as  the  cones  in  that  locality  contain  no  visual  purple, 
which  is  considered  the  organ  of  adaptation  of  the  retina.  The  inferi- 
ority of  the  macula  may  be  due,  as  has  been  suggested,  to  the  yellow 
pigmentation  of  the  macula  absorbing  a  part  of  the  blue  rays  that 
play  such  an  important  part  in  feeble  illumination.  The  period  of 
adaptation  and  the  time  it  takes  for  the  visual  purple  to  reproduce 
itself  are  about  alike,  namely,  twenty  minutes. 

After-images.  —  After-images  are  the  visual  impressions  that  per- 
sist after  the  eyes  are  closed  or  turned  away  from  the  object.  If  the 
after-image  has  a  color  complementary  to  that  of  the  object,  it  is 
spoken  of  as  a  negative  after-image,  while  if  it  is  of  the  same  color 
as  the  object  itself,  it  is  called  a  positive  after-image.  An  example 
of  the  first  kind  is  obtained  by  gazing  for  a  few  moments  at  a  colored 
surface  upon  a  white  background.  Soon  the  object  begins  to  change 
its  color  and  to  become  surrounded  by  a  border  of  its  complementary 
color. 

The  part  of  the  retina  where  the  image  of  the  colored  object  is 
formed  is  fatigued  for  the  color  in  question.  If  the  look  is  transferred 
to  a  sheet  of  white  paper,  we  perceive  an  after-image  tinged  with  the 
complementary  color  of  the  object.  This  fact  enhances  the  color- 
perception  theory  of  Hering.  To  obtain  a  positive  after-image,  close 
the  eyes  and  cover  them  with  the  hands  to  exclude  all  light.  Remain 
in  this  position  until  all  previous  impressions  have  faded  from  the 
retina.  Then  remove  the  hands  and  open  the  eyes  for  a  second 
without  changing  the  direction  of  the  gaze,  shut  them  immediately 
and  cover  them  again.  If  the  experiment  is  successful  we  will  then 
see  a  very  clear  after-image  of  the  external  object.     The  less  illu- 


176  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

mined  parts  of  the  image  first  disappear,  while  the  more  illumined  parts 
change  color,  becoming  bluish,  violet,  orange  and  so  forth.  An  after- 
image may  last  as  long  as  a  fifth  of  a  second,  as  when  one  moves  a 
piece  of  burning  wood  around,  giving  the  appearance  of  the  trail  of 
fire  familiar  to  all. 

The  Troxler  Phenomenon.  — If  we  draw  several  dots  on  a  piece  of 
white  paper  and  fix  one  of  them  for  some  time  we  will  see  first  one 
and  then  another  of  the  surrounding  dots  fade  from  view,  to  reap- 
pear after  a  little  especially  at  the  moment  of  winking  or  of  making 
a  slight  movement  of  the  eye.  This  phenomenon  was  described  at 
the  beginning  of  the  last  century  by  Troxler.  It  has  been  studied  of 
late  by  Dr.  Holth.  The  color  of  the  ground  upon  which  the  dots  are 
drawn  plays  no  part  and  when  the  dots  fade  from  the  view  the  back- 
ground is  seen  in  place  of  the  dots.  The  gap  in  the  field  is  then 
filled  in  after  the  manner  of  the  blind  spot  of  Mariotte.  If  we  fix  a 
square  on  a  chess-board,  we  will  often  notice  that  now  one  and  now 
another  of  the  surrounding  squares  will  disappear,  to  reappear  after 
a  little.  Luminous  objects  can  be  made  to  disappear  in  a  like  man- 
ner according  to  Dr.  Holth,  The  same  phenomenon  occurs  in  slowly 
moving  bodies,  so  some  care  must  be  taken  on  this  account  in  taking 
a  field  of  vision,  if  we  wish  to  perform  it  with  precision. 

The  explanation  of  this  curious  phenomenon  has  not  yet  been  ad- 
vanced. 


CHAPTER   XII  ^ 

MALIGNERING    OR    SIMULATION    OF    BLINDNESS 

At  times  patients  make  an  attempt  to  fool  the  physician  into 
believing  that,  they  are  blind  or  that  their  vision  is  very  defective. 
They  are  often  led  to  do  this  in  order  that  the  doctor  may  testify  to 
their  unfitness  for  military  service,  or  that  they  may  get  damages  from 
some  railroad  company  upon  whose  cars  they  met  with  some  acci- 
dent, and  having  nothing  to  show  for  the  damage  done,  simulate 
blindness.  It  happens  that  sailors  who  want  to  desert  their  ships  will, 
when  they  touch  land,  often  complain  of  poor  sight,  and  entering  some 
hospital  feign  blindness  until  their  ship  has  cleared  port.  We  are 
ofttimes  led  to  believe  that  the  patient  is  a  faker  from  the  surround- 
ings of  the  case. 

If,  on  examination,  the  fundi  oculorum  are  normal  in  appearance 
and  especially  if  the  pupil  of  the  supposed  Wind  eye  is  of  the  same 
size  as  its  fellow,  and  reacts,  that  is,  contracts,  when  light  is  thrown 
into  the  eye,  the  chances  are  that  the  eye  sees.  All  blind  eyes  have 
dilated  pupils,  unless  the  cause  of  blindness  is  to  be  found  posterior 
to  the  primary  optical  centers,  namely ;  the  optic  thalami,  the  cor- 
pora geniculata,  and  the  corpora  quadrigemina.  Any  lesion  anterior 
to  these  parts  in  the  path  of  the  optic  fibers  will  abolish  the  contrac- 
tion of  the  pupil  to  the  influence  of  light.  To  prove  that  the  sphinc- 
ter of  the  pupil  is  not  paralyzed,  being  the  cause  of  the  mydriasis  ; 
light  is  thrown  into  the  sound  eye,  and  if  the  pupil  of  the  supposed 
blind  eye  is  not  adherent  to  the  lens  capsule  behind  it  will  contract. 
It  is  most  likely  that  the  eye  has  some  vision  if  the  pupil  reacts  to 
exposure  to  light.  It  is  rarely  that  one  simulates  bilateral  blindness. 
It  is  often  very  difficult  to  detect  malignering.  Many  tests  have  been 
devised  for  its  detection,  and  a  knowledge  of  them  all  is  not  super- 
fluous, as  when  one  fails  the  other  may  be  tried, 
12  177 


178  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

Tests  for  Simulated  Blindness. — The  patient  is  asked  to  look  at 
his  own  hand  held  in  front  of  him  with  the  good  eye  closed.  A  blind 
man  can  do  this  through  the  muscular  sense,  that  is,  he  can  properly 
direct  his  sightless  visual  organ,  but  a  faker  knowing  that  his  good 
eye  is  closed  will  most  likely  allow  the  fellow  eye  to  wander  here  and 
there  in  search  for  the  hand  (Schmidt-Rimpler).  A  lighted  candle  is 
held  before  the  good  eye  and  then  slowly  moved  towards  the  sup- 
posed blind  eye.  The  fraud  is  detected  if  the  candle  is  seen  after  it 
is  concealed  from  the  good  eye  by  the  bridge  of  the  nose  (Cuignet). 
We  give  the  patient  some  reading  matter  and  ask  him  to  read. 
While  he  is  reading  we  hold  a  pencil  vertically  between  the  book  and 
his  eyes,  in  the  median  line.  If  he  continues  to  read  uninterruptedly 
it  is  proof  that  both  eyes  are  being  used,  while  if  the  pencil  obscures 
the  print  from  him  he  is  presumably  using  only  one  eye.  This  test 
is  not  very  reliable,  for  the  patient  may  claim  that  he  cannot  see  the 
moment  the  pencil  is  placed  in  front  of  the  book  (Cuignet). 

A  strong  convex  sphere  is  placed  before  the  sound  eye.  The  lens 
makes  the  eye  artificially  myopic.  If  a  5  D.S.  is  used  the  eye  is  ren- 
dered that  much  myopic  if  it  was  emmetropic  before.  Such  an  eye 
cannot  read  further  off  than  its  far-point,  which  in  this  case  lies  at 
(100-^5  =  20  cm.)  20  cm.  distance.  Some  print  is'then  taken  and 
held  at  or  closer  than  twenty  centimeters,  to  show  the  patient  that 
his  good  eye  is  not  screened.  As  he  reads  the  print  is  withdrawn 
further  and  further  from  the  eyes.  If  he  continues  to  read  after  the 
book  has  receded  beyond  the  far-point  of  the  sound  eye,  he  is  read- 
ing with  his  supposed  blind  eye. 

We  make  a  show  of  occupying  ourselves  with  the  good  eye  only, 
telling  the  patient  that  inasmuch  as  he  has  only  one  good  eye  left, 
it  is  wise  to  examine  it  to  see  whether  it  needs  glasses  or  not. 
that  it  is  not  well  to  put  all  the  strain  upon  the  unaided  eye.  Some 
distant  test  type  is  given  him  to  read.  While  he  reads  a  strong 
convex  spherical  lens  is  slipped  in  front  of  the  good  eye.  If  the 
patient  does  not  immediately  discover  that  he  cannot  see  so  well  he 
is  not  blind  in  the  eye  before  which  there  is  no  glass.     One  must 


MALIGNERING   OR   SIMULATION   OF   BLINDNESS.  1 79 

watch  that  both  eyes  are  always  kept  open.  Frequently  by  this 
method  one  can  ascertain  the  exact  amount  of  vision  in  the  supposed 
blind  eye. 

The  patient  is  told  to  look  at  a  candle  flame  at  twenty  feet  distance. 
Before  the  acknowledged  seeing  eye  a  Maddox  doubling  prism  is 
placed,  with  the  intersecting  line  bisecting  the  pupil.  Two  candles 
are  seen  with  the  eye  before  which  is  placed  the  prism.  We  say  to 
the  patient :  You  see  two  candles  ?  He  says  that  he  does.  The  Mad- 
dox prism  is  then  slipped  up  or  down  so  that  the  eye  only  sees 
through  the  upper  or  lower  half  of  it.  If  on  inquiry  the  patient  still 
sees  two  candles,  both  eyes  are  seeing,  one  candle  seen  by  each  eye. 
Instead  of  a  Maddox  doubling  prism,  a  simple  prism  may  be  used. 
Jt  should  be  placed  before  the  sound  eye  with  its  base  bisecting  the 
pupil,  so  that  monocular  diplopia  is  produced.  The  test  then  pro- 
ceeds as  in  the  former  case.  If  a  reading  test  is  used  for  this  exam- 
ination, we  can  compel  the  person  under  examination  to  read  some- 
times the  upper  and  sometimes  the  lower  of  the  two  paragraphs  or 
lines  and  thus  ascertain  the  visual  acuity  of  each  eye  separately  with- 
out the  patient  being  aware  of  it  (Alfred  Graefe). 

Snellen  has  constructed  letters  that  are  alternately  red  and  green. 
To  read  them  a  pair  of  spectacles  with  a  red  glass  in  one  side  and  a 
green  glass  in  the  other  is  placed  upon  the  patient.  Through  the 
red  glass  the  red  letters  alone  can  be  read  and  through  the  green 
glass  the  green  letters.  This  test  presupposes  that  the  letters  are 
made  upon  a  black  background,  for  red  letters  upon  a  white  ground 
are  invisible  through  a  red  glass,  and  the  green  ones  upon  a  white 
ground,  invisible  through  a  green  glass.  If  the  patient  has  the  red 
glass  before  the  blind  eye  and  reads  some  of  the  red  letters  his  fraud 
is  detected.  A  recent  and  a  very  complete  test  for  simulated  blind- 
ness is  that  shown  in  the  cut  on  next  page. 

DR.    PERCY    FRIDENBERG's   TEST    FOR   SIMULATING   BLINDNESS. 

This  instrument  was  devised  by  Dr.  Percy  Fridenberg,  to  reflect 
the  image  of  a  test  card  in  such  a  way  that  it  can  be  seen  by  only 


l8o  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

one  eye  at  a  time,  and  a  quantitative  demonstration  of  vision  made 
without  the  subject  of  examination  obtaining  any  clue  as  to  which 
eye  is  being  tested. 

The  mirror  is  mounted  on  a  horizontal  arm  in  such  a  way  as  to 
permit  of  varying  its  distance  from  the  test  card,  and  of  presenting 
it  alternately  to  either  eye  by  revolving  the  bearing  through  an  arc 
of  1 80°.  The  lateral  tilt  of  the  mirror  can  be  changed  at  will,  and 
is  indicated  by  a  pointer  on  a  horizontal  scale.     When  the  pointer  is 


at  90°,  the  plane  of  the  mirror  is  at  right  angles  to  the  line  of  vision 
of  the  eye  on  the  corresponding  side,  and  this  eye  sees  its  own 
image.  The  test  card  on  this  side,  however,  is  not  normal  to  the 
mirror,  and  its  reflection  is  seen  only  by  the  opposite  eye,  which  the 
subject  presumes  to  be  unconcerned  in  the  visual  act,  as  it  does  not 
appear  in  the  mirror. 

A  slight  tilting  of  the  mirror  to  the  temporal  side,  bringing  the 
pointer  to  95°  or  100°,  is  sufficient  to  reverse  the  optical  conditions 
so  that  the  test  card  is  seen  only  by  the  eye  on  the  same  side.  By 
switching  the  mirror  over  to  the  opposite  side  of  the  arm,  a  similar 
double  test  can  be  applied,  so  that  in  all  eight  variations  are  rapidly 
obtained,  as  follows  : 


MALIGNERING   OR    SIMULATION   OF    BLINDNESS.  i8l 

MIRROR  BEFORE  O.   D.  MIRROR  BEFORE  O.  S. 

95°  O.  D.  sees  right  card.  95°  Q.  S.  sees  left  card. 

90°  O.  S.       "       "        "  90°  O.  D.     "     "      " 

70°  O.  D.      "    left      "  70°  O.  S.      "  right  " 

60°  O.  S.      "       "        "  60°  O.  D.     "      "      " 

The  mirror  can  be  adjusted  laterally  to  correspond  exactly  with  the 
inter-pupillary  distance,  and  correcting  glasses  inserted  in  the  trial 
frame,  if  necessary. 

The  test  is  simple,  rapid  and  exact,  gives  no  clue  to  the  simulant, 
and  can  be  demonstrated  without  theoretical  explanations  to  the 
members  of  a  commission  or  jury. 

The  stereoscope  may  also  be  used  for  detecting  simulated  blind- 
ness. Half  pictures  are  used.  For  example  on  one  side  of  the  test 
card  is  the  picture  of  a  horse,  while  on  the  other  is  that  of  a 
jockey.  The  diaphragm  of  the  stereoscope  prohibits  the  right  eye 
from  seeing  the  picture  before  the  left  eye  and  vice  versa.  If  one 
eye  alone  sees,  either  the  horse  or  the  rider  will  be  seen,  while  if 
both  eyes  see,  the  patient  will  at  once  say  when  questioned  that  he 
sees  a  horse  with  a  man  upon  his  back.  Care  must  be  taken  that 
the  patient  does  not  close  one  eye. 

Hering's  test  of  stereoscopic  vision  is  not  practical,  as  many  have 
quite  a  good  estimation  of  depth  or  perspective  with  one  eye  alone, 
and  others  with  two  eyes  can  with  difficulty  interpret  the  test 
properly.  Hering's  test  is  that  at  the  end  of  a  long  tube  or  box 
little  pith  balls  are  dropped  first  anterior  and  then  posterior  to  a 
screen  made  of  threads  or  fine  wire.  The  patient  with  his  eye  at 
the  other  end  of  the  tube  is  asked  to  tell  each  time  a  ball  is  dropped 
whether  it  passes  in  front  of  or  behind  the  screen.  When  the  mal- 
ignerer  is  pretending  that  both  eyes  are  bhnd  it  is  very  difificult  to 
trip  him  up. 

If  the  man  complains  of  pain  in  the  eyes  at  the  same  time,  one 
may  instill  cocain  a  few  times  into  the  eyes,  and  if  the  man  is  a  faker 
he  will  not  acknowledge  that  the  anaesthetic  has  relieved  his  pain  in 
the  least.     The  following  illustrates  such  a  case  well.     An  electrician 


1 82  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

while  repairing  bumpers  in  a  power  house,  claimed  that  one  blew 
out,  causing  an  intense  flash  of  light  which  he  received  directly  into 
the  eyes.  He  was  much  frightened,  and  at  the  same  time  received 
a  little  shock  of  electricity.  For  a  day  he  was  unable  to  see,  and 
light  was  very  painful  to  the  eyes.  When  I  saw  him  all  vestige  of 
trouble  had  disappeared,  but  he  had  made  up  his  mind  that  he  would 
sue  the  railroad  company,  so  he  came  groping  into  my  office.  His 
eyes  in  all  particulars  presented  a  healthy  appearance.  He  claimed 
that  the  light  annoyed  him  so  that  he  could  not  keep  the  eyes  open. 
I  instilled  some  cocain  solution  (four  per  cent.)  and  after  several  instil- 
lations, the  pain  was  not  relieved  in  the  least.  I  gave  him  some  co- 
cain solution  to  take  home,  telling  him  to  use  it  every  two  hours. 
He  returned  and  said  that  the  medicine  had  not  done  him  a  bit  of 
good,  although  his  pupils  were  now  widely  dilated  from  the  drug. 
The  pupils  were  active  at  his  first  visit.  After  some  persuasion  his 
vision  began  to  rise  rapidly.  At  times  the  fraud  may  be  detected  by 
making  a  quick  motion  as  if  to  hit  the  patient  in  the  eye,  when  he 
will  flinch,  and  bat  the  eyes.  A  few  days  in  bed  on  low  diet,  pilo- 
carpine sweats,  or  electric  cautery,  or  a  very  strong  faradic  current 
applied  frequently  to  the  spine  will  bring  the  patient  to  terms. 


CHAPTER  XIII 

VISUAL   IMPRESSIONS 

Since  the  retinal  image  of  an  external  object  bears  a  definite  rela- 
tion to  the  object  in  regard  to  its  size,  position  and  form,  it  would 
be  expected  that  the  sensation  produced  would  correspond  to  the 
sensory  impulse,  originating  in  the  formation  of  the  retinal  image. 
We  should  expect  that  our  mental  condition  resulting  from  looking 
at  an  object,  would  correspond  exactly  to  the  retinal  image  of  the 
object.  This  is  not  the  case.  There  arise  certain  discrepancies 
between  our  perception  and  the  retinal  image,  some  having  their 
origin  in  the  retina,  some  in  the  brain,  and  others  being  of  such  a 
nature  that  it  is  difficult  to  say  where  the  discrepancy  is  introduced. 
Such  discrepancies  are  called  optical  illusions,  among  which  may  be 
mentioned  the  phenomena  of  irradiation  and  contrast. 

Irradiation. —  A  white  spot  on  a  dark  background  looks  larger 
than  a  black  spot  on  a  white  background.  This  is  to  be  especially 
noticed  when  the  object  is  somewhat  out  of  focus,  and  is  to  be  partly 
explained  by  the  formation  of  diffusion  circles,  which  encroach  in 
each  case  from  the  white  upon  the  dark,  but  besides  this  any  sensa- 
tion arising  from  a  stimulated  area  of  the  retina  gives  the  impres- 
sion of  a  larger  object  in  the  field  of  vision  when  the  rest  of  the 
retina  and  visual  apparatus  are  at  rest  than  when  they  are  simul- 
taneously excited.  The  retinal  or  central  visual  structures  seem  to 
be  thrown  into  action  sympathetically  at  the  same  time 

Contrast. — If  a  white  strip  of  paper  or  a  white  paper  figure  be  placed 
upon  a  black  background,  the  edges  of  the  figure  will  appear  whiter  than 
the  central  portions.  The  middle  of  the  figure  may  look  so  dark  that  it 
will  appear  to  be  shaded.  This  occurs  even  when  the  object  is  well  in 
focus.  The  apparent  greater  whiteness  of  the  borders  of  the  figure 
is  due  to  the  contrast  between  the  border  and  the  black  background. 

183 


1 84 


THE   EYE.    ITS   REFRACTION   AND    DISEASES. 


In  the  figure  it  will  be  noticed  that  at  the  intersections  of  the 
white  lines  there  appears  a  shadow  with  illy  defined  borders.  When 
the  attention  is  directed  to  one  of  these  spots,  it  disappears,  while 
the  other  persists. 

If  a  small  piece  of  gray  paper  be  placed  upon  a  sheet  of  green 
paper  and  both  covered  with  a  piece  of  tissue  paper,  the  gray  will 
appear  to  be  of  a  pink  color,  the  complementary  color  to  green.  If 
white  paper  is  used  instead  of  gray  this  effect  of  contrast  is  absent. 

The  contrast  will  disappear  if  a  broad 
black  line  be  drawn  around  the  small 
piece  of  gray  paper,  so  as  to  isolate 
it  from  the  ground  color.  If  a  book 
be  placed  vertically  upon  a  sheet  of 
white  paper  and  illumined  on  one  side 
by  the  sun  and  on  the  other  side  by  a 
candle,  two  shadows  will  be  produced. 
The  one  cast  by  the  sun  is  illumined 
by  the  yellow  light  of  the  candle,  and 
the  one  cast  by  the  candle  will  be 
illumined  by  the  white  light  from  the 
sun.  The  first  appears  yellow,  the  latter  however  appears,  not  white, 
but  blue,  a  color  complementary  to  that  of  the  candle  light  that  sur- 
rounds it.  If  the  candle  is  moved  the  blue  light  disappears.  If  some 
part  of  the  area  illumined  by  the  candle  is  looked  at  through  a  tube 
blackened  on  the  inside,  the  blue  color  disappears  because  there  can 
be  no  contrast,  but  if  the  edge  of  the  area  is  looked  at  through  the 
tube  the  blue  color  reappears,  as  then  there  is  a  contrast  formed 
between  it  and  the  white  paper  around. 

Our  judgments  of  a  color  depend  a  great  deal  upon  the  color  of 
the  surrounding  medium,  or  upon  simultaneous  contrast,  as  in  the 
two  experiments  mentioned  above.  The  phenomenon  of  contrast  is 
due  to  a  false  conception  of  white.  A  piece  of  paper  that  is  white 
by  daylight  is  still  considered  white  by  us  when  illumined  by  the  yel- 
low light  of  a  candle  or  by  the  red  light  of  a  coal  fire.     Javal  pointed 


VISUAL   IMPRESSIONS.  1 85 

out  that  we  consider  all  objects  as  white  that  reflect  or  return  the 
most  light,  no  matter  what  the  color  of  the  light  may  be.  If  the  real 
color  of  the  paper  differs  much  from  its  color  by  daylight,  which  fact 
we  unconsciously  recollect ;  it  seems  white  to  us  with  a  faint  colored 
tone.  Through  a  red  glass,  when  the  eye  receives  only  red  rays  of 
light,  a  piece  of  white  paper  appears  reddish  white.  We  may  regard 
the  zero  of  our  color  sensations  diplaced  and  with  it  the  entire  scale. 
If  the  yellowish-white  shadow  that  illuminated  the  screen  in  the  ex- 
periment with  the  book,  mentioned  above,  appears  white  to  us  it  is 
not  strange  that  we  should  consider  the  white  light  that  illuminates 
the  other  shadow  as  blue,  that  is  less  yellow  than  the  screen. 

The  colors  of  after-images  are  due  to  what  is  known  as  successive 
.  contrast,  and  are  explained  by  the  retina  becoming  fatigued  for  the 
colors  in  question,  and  by  regeneration  giving  rise  to  the  comple- 
mentary color.     (See  article  upon  After-images.) 

The  Physiological  Blind  Spot  and  the  Filliftg  Up  of  I  tin  the  Visual 
Field. —  The  optic  nerve  entrance  is  blind;  it  is  even  devoid  of  light 
perception.  As  has  been  seen  it  lies  to  the  nasal  side  of  the  center 
of  the  retina  about  fifteen  degrees,  and  a  little  above  it.  The  pres- 
ence of  this  blind  spot  (Mariotte's)  can  be  easily  demonstrated  by  the 
following  plan.  Upon  a  card  make  two  dots  several  inches  apart. 
Take  the  card  in  the  right  hand,  and  keeping  the  left  eye  closed  look 
steadily  at  the  left-hand  dot  as  you  cause  the  card  to  approach  the 
eye.  In  a  certain  position  according  to  the  distance  of  the  dots  apart, 
the  right-hand  dot  on  the  card  will  disappear  from  view.  It  will  ap- 
pear again  if  the  card  or  the  eye  is  moved  a  little.  The  image  of  the 
dot  upon  which  the  eye  is  fixed  falls  upon  the  macula,  and  that  of 
the  other  dot  falls  upon  the  optic  nerve  entrance. 

Notwithstanding  this,  we  are  not  conscious  of  any  gap  in  our  vis- 
ual field.  Some  of  the  printed  matter,  when  we  are  reading,  must 
throw  its  image  upon  the  blind  optic  papilla,  but  no  gap  is  noticed. 
We  would  not  expect  to  see  a  black  area  or  patch,  for  black  is  the 
sensation  produced  by  the  absence  of  light  from  structures  that  are 
sensitive  to  lio-ht.    There  must  be  a  visual  organ  to  see  black.    Visual 


1 86  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

organs  (rods  and  cones)  are  absent  at  the  optic  nerve  entrance,  and 
it  is  in  no  way  affected  by  the  light  that  falls  upon  it.  The  reason 
no  gap  is  perceived  in  the  field  is  that  we  refer  the  sensation  pro- 
duced by  two  points  lying  upon  opposite  margins  of  the  disc,  as 
coming  from  two  points  lying  very  close  together,  as  we  have  no  in- 
dication of  the  amount  of  space  that  separates  them.  The  existence 
of  the  blind  spot  is  of  little  importance,  inasmuch  as  it  is  out  of  the 
way  of  direct  vision,  and  the  image  of  an  object  could  never  fall  upon 
the  blind  spot  of  the  two  eyes  at  one  time,  so  the  one  eye  is  able  to 
fill  the  deficiency  of  the  other  in  this  regard.  Again,  images  that  are 
formed  on  the  periphery  of  the  retina  as  far  removed  from  the  center 
as  the  optic  disc  are  seen  so  indistinctly  that  if  a  gap  in  the  field 
was  present  at  that  locality  it  would  most  likely  not  be  noticed.  We 
may  have  a  visual  sensation  in  the  entire  absence  of  light  Any 
stimulation  or  irritation  of  the  retina  or  optic  nerve  may  give  rise  to 
the  sensation  of  light.  Pressure  upon  the  eyeball  gives  rise  to  the 
appearance  of  colored  rings  of  light,  known  as  phosphenes.  A  blow 
upon  the  eye  causes  a  flash  of  light.  The  optic  nerve  answers  to  a 
stimulus  ot  any  kind  by  causmg  the  sensation  of  light  and  not  pain. 
Complex  and  coherent  visual  images  may  arise  in  the  brain  without 
any  corresponding  objective  cause.  These  phantoms  or  ocular  spec- 
tra have  a  realness  quite  as  striking  as  those  of  ordinary  visual  per- 
ceptions. They  are  seen  with  the  eyes  open  and  closed.  The  phan- 
toms seen  in  a  case  of  delirium  tremens  are  a  good  example  of  ocu- 
lar spectra. 

Appreciation  of  the  Apparent  Size  and  Distance  of  an  Object.  — 
With  the  eye  alone  we  can  only  estimate  the  apparent  size  and  dis- 
tance of  an  object.  We  can  tell  what  part  of  the  field  it  occupies, 
and  by  comparing  the  visual  angles  of  two  objects  estimate  their 
relative  sizes.  The  real  size  of  an  object  is  determined  by  other 
means.  Our  perception  of  the  apparent  size  of  an  object  may  be  so 
modified  that  it  cannot  be  relied  upon.  The  moon  for  instance  looks 
to  be  of  different  sizes  to  different  individuals.  Any  ocular  decep- 
tion (as  has  been  noted)  is  called  an  optical  illusion.     Thus,  let  a 


tmm 


VISUAL   IMPRESSIONS.  1 87 

line  AB  be  divided  into  two  equal  parts,  A  C  and  CB.  Subdivide  por- 
tion AC  into  equal  parts  by  distinct  marks.  It  will  now  be  noticed 
that  the  portion  subdivided  appears  the  longer,  that  is,  AC  appears 
longer  than  BC 

If  two  squares  A  and  B  of  equal  dimensions  are  marked  with 
stripes  running  cross-wise  in  the  one  and  vertically  in  the  other,  the 
former  will  appear  higher  and  the  latter  broader  than  it  really  is. 

In  order  to  observe  this  phenomenon  cover 
square  A  and  it  will  be  noticed  that  square 
B  appears  to  be  broader  than  long,  while  A 
appears  taller  than  broad  ;  when  B  is  cov- 
ered. The  moon  looks  larger  on  the  hori- 
zon, as  then  it  can  be  easily  compared  with  the  size  of  terrestrial 
bodies.  A  short  man  and  a  tall  one  side  by  side  causes  the  for- 
mer to  appear  shorter  and  the  latter  taller  than  he  really  is  by  con- 
trast. On  the  other  hand,  absence  of  comparison  may  lead  us  to 
suppose  that  an  object  is  larger  than  it  is.  A  man  in  a  fog  looks 
larger  than  he  is.  Seeing  him  indistinctly  we  imagine  that  he  is 
further  off  than  he  is  ;  subconsciously  connecting  the  size  of  the 
visual  angle  he  subtends  with  the  indistinctness  with  which  we  see 
him  our  conclusion  is  drawn  that  he  must  be  a  very  large  man. 

On  the  other  hand,  distant  objects  in  a  very  clear  atmosphere  are 
judged  to  be  nearer  than  they  really  are,  as  they  are  seen  so  dis- 
tinctly. Distances  upon  the  water  are  very  deceptive,  appearing 
shorter  than  they  are,  as  there  are  no  intervening  objects.  Our 
previous  experience  is  the  most  potent  factor  in  our  estimations  of 
size  and  distance  ;  our  visual  perceptions  with  our  visual  judgments. 
Visual  yudgments.  —  Binocular  vision  or  the  seeing  with  two  eyes 
is  of  use  to  us  inasmuch  as  the  one  eye  can  fill  up  the  insufficiencies 
of  the  other.  Over  and  above  the  filling  up  of  the  blind  spot  one 
eye  supplies  that  part  of  the  visual  field  that  is  lacking  to  the  other. 
The  great  use  of  binocular  vision  is  however  to  inform  us  of  the  size, 
shape  and  distance  of  objects  from  the  eyes  and  their  distance  from 
each  other. 


1 88  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

ytidgmcnt  of  Distance  and  Sise.  —  By  the  association  of  visual  sen- 
sations with  those  of  touch  and  handHng  of  objects,  and  with  the 
sensation  derived  from  the  movements  of  the  eyeballs  necessary  to 
make  any  such  part  of  the  field  as  corresponds  to  a  particular  object 
distinct,  we  are  led  to  form  judgments  which  gradually  become  fixed 
in  our  sensoria.  Even  with  one  eye  we  can  to  a  certain  extent  form 
some  judgment,  not  only  as  to  the  position  of  an  object  in  a  plane  at 
right  angles  to  our  visual  axis,  but  also  as  to  its  distance  along  the 
visual  axis.  If  the  object  is  near  we  must  accommodate  for  it,  to 
render  it  distinct ;  if  far  away,  we  must  relax  our  accommodation  to 
make  it  clear  to  us.  The  muscular  sense  of  this  effort  through  the 
ciliary  muscle  enables  us  to  judge  somewhat  of  the  distance  of  the 
object.  We  judge  of  the  distance  separating  two  objects  by  the 
amount  of  innervation  necessary  for  the  ocular  muscles  to  turn  the 
eyes  from  the  one  object  to  the  other.  Looking  directly  at  the  ob- 
ject 0,  another  object  /  at  its  side  casts  its  image  upon  the  periph- 
eral parts  of  our  retinas.  The  distance  separating  the  images  of  the 
external  objects  regulates  the  amount  of  innervation  sent  to  the 
eyes,  in  order  that  they  may  be  promptly  and  exactly  directed  from 
the  one  object  to  the  other.  That  the  amount  of  innervation  needed 
to  accomplish  this  is  the  real  estimate  of  the  separation  of  the  two 
objects  there  is  no  doubt. 

If  a  patient  with  a  paralysis  of  the  right  external  rectus  muscle 
closes  his  left  eye  and  is  told  to  look  at  an  object  to  the  right,  he 
supplies  the  necessary  will  power,  but  the  innervation  to  the  right 
external  rectus  muscle  is  at  fault  so  the  eyeball  does  not  move. 
The  patient  thinks  that  it  has,  and  there  results  a  false  projection 
and  orientation.  If  he  is  told  to  move  his  finger  rapidly  to  the  right 
and  touch  the  object,  he  most  often  moves  the  finger  too  far,  as  he 
judges  of  the  distance  of  the  object  to  the  right  from  the  amount  of 
innervation  sent  to  the  paralytic  muscle  plus  that  caused  by  false 
orientation. 

In  the  figure  the  right  external  rectus  muscle  is  considered  para- 
lytic.     O  is  an  object  to  the  right  of  the  eyes.     In  the  left  eye  the 


VISUAL    IMPRESSIONS. 


189 


image  of  O  falls  upon  the  macula  as  the  eye  is  able  to  turn  towards 
it  but  the  right  eye  does  not  move,  so  the  image  of  O  falls  to  the 
left  of  the  macula.     M  is  the  macula  in  each  ;  N,  the  nodal  point. 


The  individual  supposes  that  the  right  eyeball  has  turned  towards 
the  object,  and  inasmuch  as  the  nasal  retina  is  influenced,  that  the 
object  must  lie  further  to  the  right  than  it  does.  O'  is  the  apparent 
position  of  the  object  O  to  the  eye  R,  for  if  when  the  eye  is  turned 
towards  the  object  O,  an  object  that  forms  its  image  at  M'  must  be 
at  O'. 

The  close  association  of  touch  and  sight  in  forming  judgments  of 
distances  and  size  is  illustrated  in  those  born  blind  but  who  have 
afterwards  received  their  sight  through  an  operation.  Such  individ- 
uals are  at  first  unable  to  properly  estimate  distances.  If  a  foot-rule 
is  shown  it  will  be  imagined  to  be  much  longer  or  shorter  than  it 
really  is,  to  the  surprise  of  the  individual  when  he  is  allowed  to 
handle  it.  Likewise  they  cannot  tell  the  shape  of  an  object,  for  ex- 
ample whether  it  is  spherical  or  cuboidal.  These  facts  are  fixed  in 
the  mind  of  the  growing  child  through  the  association  of  touch  and 
sight. 

Knowing  the  narrow  range  of  accommodation  and  the  slight  mus- 


190  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

cular  effort  that  it  entails,  one  can  easily  see  that  all  monocular  judg- 
ments are  subjected  to  much  error.  The  person  who  tries  to  thread 
a  needle  without  using  both  eyes  knows  how  difficult  it  is  to  estimate 
distances  properly  with  only  one  eye.  When  the  object  is  near  and 
both  eyes  are  being  used,  we  converge  the  visual  axes  of  the  two 
eyes  towards  the  object ;  and  when  distant,  we  bring  them  to  paral- 
lelism. This  contraction  of  the  extraocular  muscles  gives  us  a  sense 
that  aids  the  muscular  sense  of  accommodation,  to  estimate  properly 
the  distance  of  an  object.  If  by  any  means  the  amount  of  accom- 
modation needed  to  bring  an  object  into  focus  is  lessened,  the  object 
appears  to  have  receded,  and  if  more  accommodation  is  used  than 
one  is  accustomed  to  use  for  a  given  distance,  the  object  looked  at 
appears  nearer  than  it  is.  The  same  is  the  case  with  the  convergent 
effort,  that  is  the  more  convergence  is  needed  to  bring  the  object 
clearly  into  view  before  the  two  eyes,  the  nearer  the  object  is  judged 
to  be.  These  facts  are  well  illustrated  in  the  stereoscope,  where  a 
picture  at  very  short  range  is  looked  at  through  convex  glasses  and 
prisms  so  that  no  accommodation  or  convergence  is  required.  The 
pictures  therefore  appear  to  be  at  a  great  distance  from  the  eyes. 
The  judgment  of  the  size  of  an  object  is  closely  connected  with  that 
of  distance.  Our  perceptions  gained  exclusively  from  the  field  of 
vision  go  no  further  than  the  apparent  size  of  an  object.  The  real 
size  of  an  object  is  only  rightly  conjectured  from  the  apparent  size 
of  an  object  when  its  distance  from  the  eyes  is  taken  into  account. 

Thus :  When  there  appears  in  our  field  of  vision  the  form  of  a 
man  ;  knowing  the  ordinary  size  of  a  man,  we  infer  from  his  appar- 
ent size  the  distance  of  the  man  from  us.  If,  on  the  other  hand,  we 
have  an  estimate  of  the  distance  at  which  the  man  is  through  the 
presence  of  intervening  objects  or  from  experience,  we  judge  of  his 
real  size  from  the  apparent  size  he  has  at  that  distance.  An  image 
upon  a  screen  when  gradually  enlarged  appears  to  approach,  inas- 
much as  all  approaching  objects  subtend  progressively  larger  and 
larger  visual  angles  as  they  draw  nearer.  We  have  subconsciously 
connected  the  apparent  increase  in  size  of  an  object  with  its  approach 


VISUAL   IMPRESSIONS.  I91 

since  early  childhood,  and  therefore  any  object  that  is   increasing 
gradually  in  size  appears  to  be  moving  forward  and  vice  versa. 

Judgment  of  Perspective  or  Depth  in  a7i  Object,  or  Stereoscopic 
Visioft. —Wh^n  we  look  at  a  square  all  parts  of  it  are  at  the  same 
distance  from  us  ;  all  parts  are  equally  well  focused  whether  we  look 
at  it  with  one  or  two  eyes.  When,  on  the  other  hand,  we  behold  a 
cube,  we  realize  that  all  its  parts  are  not  at  one  distance  from  us,  as 
we  are  compelled  to  accommodate  for  successively  different  portions, 
to  bring  them  into  view.  Perhaps  an  adjustment  of  the  eyes  to  this 
side  or  that  is  necessary.  From  this  effort  on  the  part  of  the  eyes 
to  see  different  parts  of  the  body  clearly,  we  form  the  idea  of  solidity 
in  the  cube,  or  that  of  perspective  or  depth,  that  is,  that  all  parts  of 
the  object  do  not  lie  in  the  same  plane.  Our  idea  of  solidity  is  much 
more  correct  when  both  eyes  are  used,  just  as  in  the  case  of  the  esti- 
mation of  the  distance  of  an  object,  the  muscular  sense  of  the  eye- 
ball aiding  the  accommodative  sense.  We  are  much  assisted  by  the 
arrangement  of  the  light  and  shade  in  an  object  when  judging  of  its 
shape,  as  a  depression  may  appear  to  be  an  elevation  by  the  proper 
arrangement  of  light  and  shade  as  well  as  by  the  linear  perspective 
of  the  object.  For  single  binocular  vision  it  has  been  noted  that  an 
object  in  space  must  form  its  image  upon  the  corresponding  parts 
of  the  two  retinas.  This  is  not  true  in  stereoscopic  vision,  however. 
The  above  is  only  true  of  objects  or  portions  of  objects  occupying 
one  plane,  and  not  those  having  solidity  or  perspective.  Each  eye 
projects  out  into  space  the  area  of  retinal  stimulation  and  places  the 
object  on  a  line  that  passes  through  its  nodal  point.  This  line  con- 
nects the  object  and  its  retinal  image.  If  the  projected  images  join 
end  to  end  and  side  to  side,  a  solid  or  stereoscopic  picture  is  built 
up.  The  image  of  any  solid  body  in  the  right  eye  cannot  be  exactly 
like  that  that  falls  upon  the  retina  of  the  left  eye,  though  both  are 
combined  into  a  single  visual  perception.  The  right  eye  sees  a  little 
more  on  the  right  of  the  object  than  the  left  eye  and  vice  versa. 
'  The  truncated  pyramid  P,  when  looked  at  in  the  median  line  in 
front  of  the  eyes,  forms  a  retinal  image  the  shape  of  R  in  the  right 


192 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


eye,  and  in  the  left  eye  the  retinal  image  is  the  shape  of  L.  Both 
together  after  projection  make  the  appearance  of  P.  It  may  be  sup- 
posed that  the  judgment  of  solidity  which  arises  when  two  dissimilar 
images  are  thus  combined  in  one  perception  was  due  to  the  fact  that 
all  parts  of  the  two  images  cannot  fall  upon  corresponding  parts  of 


the  two  retinas  at  the  same  time,  and  that  therefore  the  combination 
of  the  two  needs  some  movement  of  the  eyes.  Thus,  if  figure  L  is 
placed  upon  R,  the  two  bases  will  coincide  when  the  apices  do  not 
and  vice  versa  ;  hence  when  the  bases  fall  upon  any  particular  part, 
the  apices  will  not  be  combined  in  a  single  image,  and  there  must 
be  a  slight  but  rapid  movement  of  the  eyes,  that  they  may  be 
combined.  That  no  such  movement  is  necessary  is  proven  by  the 
fact  that  when  a  solid  body  is  illumined  by  an  electric  spark  too 
quick  to  allow  of  the  movement  of  the  eyes,  the  solidity  is  easily 
recognized.  The  fusion  of  images  falling  upon  non-corresponding 
parts  of  the  two  retinas  is  the  operation  of  the  cerebrum,  resulting 
in  an  ocular  judgment.  If  the  images  of  two  surfaces,  one  black 
and  the  other  white  be  made  to  fall  upon  corresponding  parts  of  the 
two  retinas,  the  perception  is  not  always  a  fusion  of  the  two  colors, 
that  is  a  gray,  but  a  sensation  is  produced  similar  to  that  when  a 
polished  surface  is  looked  at,  that  is  the  surface  appears  brilliant. 
The  reason  of  this  is  because  when  we  look  at  a  polished  surface, 
more  light  enters  the  one  eye  than  the  other  according  to  the  incli- 
nation of  the  mirror  ;  hence  we  associate  an  unequal  stimulation  of 
the  two  retinas  with  a  polished  surface.  When  two  colors  of  dif- 
ferent hue  are  made  to  stimulate  the  same  area  of  retina  in  the  two 
eyes,  the  resulting  color  is  not  the  fusion  of  the  two,  as  when  both 


VISUAL   IMPRESSIONS.  1 93 

fall  upon  the  same  area  of  a  single  retina,  but  first  the  one  color  and 
then  the  other  is  seen,  immediate  tints  being  passed  through.  The 
change  of  the  color  is  frequent.  This  phenomenon  is  spoken  of  as 
the  struggle  of  the  two  fields. 

The  change  from  one  color  to  the  other  may  arise  from  the  dif- 
ficulty of  accommodating  for  the  two  at  the  same  time.  If  the  two 
eyes,  one  of  which  is  regarding  a  red  object  and  the  other  a  blue  one, 
be  accommodated  for  red  rays,  the  red  will  overlap  the  blue,  and  the 
sensation  produced  will  be  red  and  vice  versa.  For,  as  the  rays  of 
the  spectrum  are  of  different  refrangibility,  the  amount  of  accommo- 
dation needed  for  a  certain  color  is  different  from  that  needed  for 
another  color.  The  blue  end  of  the  spectrum  needs  less  accommo- 
dation to  be  seen  than  the  red  end,  as  the  blue  rays  are  refracted 
more  in  passing  through  the  dioptric  media  of  the  eyeball. 

The  Impressions  of  the  Two  Maculas  are  Projected  Towards  the 
Same  Place  in  Space.  — When  both  eyes  are  properly  directed,  each 
towards  the  object,  this  is  not  surprising,  but  the  fact  is  the  same 
when  the  two  eyes  do  not  fix  the  same  object,  as  is  seen  in  stereo- 
scopic exercises.  The  following  experiment  of  Tscherning  illustrates 
this  fact.  It  is  necessary  to  be  able  to  squint  in  order  to  perform  the 
experiment.  One  can  cause  himself  to  squint  externally,  by  pinch- 
ing up  a  piece  of  skin  near  the  outer  canthus  of  the  eye,  and  then 
trying  to  look  in  the  opposite  direction.  The  conjunctiva  is  drawn 
tightly  across  the  eyeball  by  pinching  up  the  skin  and  the  eyeball 
prohibited  from  moving  inwards  towards  the  nose  properly.  One 
eye  is  closed  and  with  the  other  one  a  lighted  candle  is  looked  at  for 
a  few  minutes,  long  enough  to  produce  an  after-image.  We  then  fix 
a  certain  point  with  the  eye  that  was  closed  while  an  attempt  is  made 
to  squint.  The  after-image  in  the  squinting  eye  will  always  place 
itself  upon  the  point  of  fixation,  no  matter  how  much  the  visual  lines 
may  converge  or  diverge.  If  we  behold  a  near  object  with  both 
eyes,  a  more  distant  one  appears  doubled  ;  as  two,  and  vice  versa. 
If  we  hold  one  finger  behind  another  at  a  distance  of  two  feet  and 
then  accommodate  first  for  the  one  finger  and  then  for  the  other,  this 
13 


194  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

fact  is  made  evident,  that  the  finger  out  of  focus  appears  doubled. 
This  phenomenon  is  called  physiological  binocular  diplopia,  and  was 
first  described  by  Alhazon.  The  suppression  of  the  image  in  one 
eye  plays  an  important  part  in  binocular  vision.  It  is  this  fact  that 
makes  physiological  binocular  diplopia  unobserved  unless  the  atten- 
tion is  called  to  it.  According  to  Dr.  Javal  it  is  the  image  that  occu- 
pies the  smallest  amount  of  retinal  surface  that  disappears.  In  the 
majority  of  cases  it  is  the  image  of  the  less  developed  eye,  the  one 
that  is  used  less  frequently,  that  is  suppressed. 

Physiological  diplopia  manifests  itself  because  the  different  position 
of  the  two  eyes  is  not  mentally  taken  into  account.  We  cannot  tell 
without  some  examination  which  image  belongs  to  the  right  and 
which  to  the  left  eye.  Every  visual  impression  from  one  or  both 
eyes  is  referred  to  a  single  visual  center,  which  corresponds  to  the 
right  or  to  the  left  eye  in  most  cases,  but  in  ideal  binocular  vision 
should  correspond  to  a  point  midway  between  the  two  eyes.  We 
should  see  objects  in  space  in  their  true  position  by  having  regard 
of  this  center  of  reference. 


CHAPTER   XIV 

ENTOPTIC    PHENOMENA 

Objects  on  the  interior  of  the  eyeball  may,  when  light  enters  the 
pupil,  cast  shadows  upon  the  sensitive  layer  of  the  retina,  and  thus 
be  perceived.  Listing  called  the  examination  of  objects  upon  the  in- 
terior of  our  own  eyes  entoptic  observation.  If  a  clear  sky  is  looked 
at  through  a  pinhole  in  a  card  held  near  the  anterior  focal  point  of 
the  eyeball,  that  is  about  15  mm.  anterior  to  the  cornea,  or  if  a  light 
at  the  distance  of  about  5  m.  be  viewed  through  a  strong  convex  lens 
(spherical),  held  at  two  or  three  inches  in  front  of  the  eye,  a  bright 
disc  of  light  will  be  seen  limited  by  the  shadow  of  the  border  of  the 
pupil,  upon  which  certain  things  are  visible. 

The  traces  of  the  lids  upon  the  cornea  may  be  seen  by  half  closing 
the  eyes.  These  horizontal  lines  caused  by  the  wrinkling  of  the  epi- 
thelium of  the  cornea  remain  an  instant  after  the  pressure  has  ceased, 
and  if  the  pressure  is  prolonged  it  leads  to  an  irritable  condition  called 
tarsal  asthenopia.  According  to  George  Bull,  tarsal  asthenopia  is 
often  made  very  pronounced  by  reading  while  lying  upon  the  back. 
By  rubbing  the  eye  the  luminous  area  appears  speckled,  due  to  irregu- 
larities of  the  cornea,  which  soon  disappear.  The  tears  and  drops 
of  mucus  and  particles  of  dust  can  be  seen  to  move  across  the  cornea 
from  below  upwards.  Certain  long  striae  are  seen  running  from 
above  downwards,  on  winking  the  lids.  These  are  caused  by  tears 
near  the  lid  borders  assuming  the  form  of  a  prism  with  a  concave 
surface  ;  the  eyelashes  are  also  distinctly  seen. 

In  using  the  microscope  all  have  noticed  that  at  times  the  lashes 
seem  to  get  in  the  way  of  seeing.  The  crystalline  lens  or  some  of 
its  portions  may  be  seen  if  the  opening  used  is  very  small,  the  light 
being  homocentric.  In  the  normal  lens  the  radiating  star-figure  and 
certain  round  objects  like  hyaline  globules  can  be  observed.     These 

195 


196  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

are  seen  best  in  later  life.  The  beginning  of  cataract  in  one's  own 
eye  can  be  seen  in  this  manner  (Donders).  By  closing  and  opening 
the  eye  the  action  of  the  pupil  to  light  is  well  observed.  When  the 
eye  is  directed  towards  the  sky  or  any  surface  of  uniform  brightness, 
as  a  sheet  of  white  paper  upon  which  the  sun  is  shining,  the  field  is 
seen  to  be  filled  with  little  bright  bodies  moving  with  considerable 
rapidity,  and  in  more  or  less  regularly  curved  lines.  The  uniformity 
of  their  movements  suggests  that  they  are  confined  to  certain  definite 
channels.  These  bodies  are  called  muscae  volitantes  ;  they  frequently 
cause  alarm  to  the  observer  when  seen  for  the  first  time.  They  are 
exaggerated  in  neurasthenia  and  are  seen  among  its  earlier  symp- 
toms. 

These  bodies  are  supposed  by  some  to  be  floating  cells  and  fibers 
in  the  vitreous  humor.  They  have  no  pathological  significance.  They 
can  be  studied  to  a  better  advantage  if  the  observer  looks  through  a 
piece  of  cobalt  blue  glass.  These  bodies  are  also  called  Bowditch's 
bodies.  Dr.  Willets  gives  a  number  of  reasons  which  seem  conclu- 
sive to  him  as  well  as  to  others  that  these  bodies  are  the  white  corpus- 
cles of  the  corneal  circulation.  Gould  suggests  that  all  positive  en- 
toptic  sensations  be  called  phoses  and  all  negative  ones  aphoses. 

The  latter  authority  is  convinced  that  the  bodies  (phoses)  described 
and  named  after  Bowditch,  and  the  so-called  spontaneous  phosphenes 
of  the  retina  are  due  to  a  reflection  from  the  corpuscles  of  the  retinal 
capillaries  varying  in  appearance  according  to  the  method  of  obser- 
vation, illumination,  etc. 

The  retinal  vessels  may  be  seen  by  several  methods  :  (a)  If  in  a 
darkened  room,  a  lighted  candle  is  held  to  the  side  of  and  a  little  in 
front  of  the  eye,  while  the  observer  looks  straight  ahead  into  the 
darkness  ;  the  retinal  vessels  will  come  into  view  as  dark  lines  on  a 
yellowish  background,  and  they  appear  to  move  whenever  the  candle 
is  moved.  The  black  lines  running  the  course  of  the  vessels  are  the 
shadows  of  the  retinal  vessels  thrown  upon  the  percipient  layer  of 
the  retina,  lying  posterior  to  the  vessels,  {d)  If  a  stenopaic  opening 
held  between  the  eye  and  the  sky  is  kept  in  motion,  the  vessels  are 


ENTOPTIC    PHENOMENA. 


197 


distinctly  seen,  even  the  smallest  around  the  macula,  {c)  If  a  strong 
light  is  focused  upon  the  sclera  as  far  back  as  possible  and  moved 
from  side   to   side,   the  same   phenomena  occur. 

The  figure  explains  the  manner  in  which  the 
retinal  vessels  are  seen  when  the  light  is  focused 
upon  the  sclera.  L  and  L'  are  two  positions  of 
the  convex  lens ;  /  and  /',  the  shadows  cast  by  the 
vessel  K 

Miiller  measured  the  movement  of  the  retinal 
vessels  projected  upon  a  surface  at  a  known  dis- 
tance, and  the  movement  of  the  light  on  the  sclera 
which  produced  the  excursion,  and  calculated  the  distance  that  the  sen- 
sitive layer  of  the  retina  must  lie  behind  the  retinal  vessels.  His 
results  coincide  very  closely  with  the  actual  distance  between  the 
vessels  and  the  rods  and  cones.  Konig  and  Zumft  claim  that  dif- 
ferent colors  are  perceived  at  different  levels  of  the  retina,  and 
apply  this  principle  to  color-vision.  They  say  that  violet  is  perceived 
by  the  m.ost  anterior  and  red  by  the  most  posterior  sensitive  layer 
of  the  retina.  We  do  not  perceive  the  shadows  cast  by  the  retinal 
vessels  upon  the  rods  and  cones  under  ordinary  conditions,  as  the 
brain  has  learned  not  to  regard  them,  to  suppress  their  images. 
When  light  is  caused,  however,  to  enter  the  eyeball  obliquely  the 
shadows  are  cast  upon  portions  not  accustomed  to  the  condition  and 
therefore  are  seen.  Or,  according  to  Muller,  the  light  enters  the 
eye,'  illuminates  the  retina  over  a  certain  area,  which  by  reflection 

illuminates    another   portion    in    which    the 
shadows  are  perceived. 

The  shadows  cast  by  the  retinal  vessels 
can  also  be  perceived  if  light  be  focused 
upon  the  anterior  portion  of  the  sclera  with 
a  convex  lens  as  noted  above.  If  the  ob- 
ject of  entoptic  observation  is  behind  the 
plane  of  the  iris  it  will  move  in  the  direction  of  the  visual  axis  ;  con- 
trary to  it ;  if  anterior  to  the  plane  of  the  iris. 


198 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


Light  enters  the  eyeball  along  the  path  x.  Striking  the  fundus  at 
the  point  i^  it  is  reflected  towards  V.  The  vessel  V  in  the  retina 
consequently  casts  its  shadow  upon  the  sensitive  layer  of  the  retina 
behind  it  at  V. 

In  the  figure  A,  let  N  be  the  nodal  point  of  the  eyeball ;  O  and  O' 
two  opacities,  one  anterior  and  the  other  posterior  to  the  plane  of 
the  iris.  Light  entering  the  eye  from  the  candle,  throws  a  shadow 
of  each  upon  the  retina  at  O" .     The  eye  therefore  projects  each  of 

them  in  the  direction  of  the  source  of 
light.  In  figure  B,  the  eyeball  is  rep- 
resented turned  up.  The  opacity  ante- 
rior to  the  iris,  that  is  O,  now  throws  its 
shadow  upon  the  fundus  at  0"\  which 
the  brain  supposes  corresponds  to  an 
object  along  a  line  drawn  from  the  point 
of  stimulation  through  the  nodal  point 
forward,  that  is  direction  0"'x,  so  that 
when  the  eye  has  moved  up  the  ob- 
ject appears  to  have  descended.  The 
corpuscle  behind  the  iris  throws  its 
shadow  upon  the  fundus  at  point  O" , 
which  is  projected  out  into  space  along 
line  0"x'.  The  opacity  appears  to 
have  moved  in  the  same  direction  as 
the  eye. 
Entoptic  observation  may  be  used  to  detect  slight  movements  of 
the  eyeball  which  would  be  difficult  if  not  impossible  to  detect  by  any 
other  means.  For  this  purpose  Dr.  Tscherning  constructed  an  in- 
strument which  he  called  the  entoptoscope.  It  consists  of  a  circular 
piece  of  a  hollow  sphere  made  of  brass.  Across  the  concavity  of 
the  cap  are  stretched  two  strings,  as  cords  of  the  arc  ;  at  the  point 
where  the  strings  cross  is  made  a  stenopaic  opening  in  the  brass  cap. 
The  whole  is  mounted  upon  an  upright  and  attached  to  a  mouth 
piece  to  be  held  between  the  teeth.     When  this  instrument  is  held 


ENTOPTIC    PHENOMENA. 


199 


between  the  teeth  and  we  look  towards  the  sky  we  see  an  entoptic 
field  containing  the  image  of  the  crossed  threads  much  magnified. 
A  certain  point  in  the  cross  is  selected  for  a  fixation  point.  The 
position  of  the  cross  is  invariably  dependent  upon  that  of  the  head, 
if  therefore  we  observe  a  displacement  of  the  cross  in  the  entoptic 
field  it  is  due  to  a  displacement  of  the  eyeball  as  a  whole.  It  can  be 
proven  with  this  instrument  that  the  eyeball  is  elevated  a  little  when 
the  eye  is  closed  or  when  we  wink  and  depressed  somewhat  when 
the  eye  is  opened  widely.  When  the  head  is  tilted  a  little  to  one 
side  the  eyeball  is  found  to  undergo  a  slight  displacement  in  the 
direction  of  its  weight. 

These  phenomena  are  made  more  striking  when  eserine  is  in- 
stilled, as  then  the  field  is  much  smaller.  The  displacement  of  the 
cross  will  then  reach  as  much  as  one  third  of  the  entire  field.  In 
order  to  determine  the  distance  of  an  object  of  entoptic  observation 
from  the  retina,  Brewster  used  two  luminous  points.  Two  circles  of 
diffusion  are  then  seen  which  partly  overlap,  and  each  object  within 
the  eye  produces  two  shadows.  The 
distance  between  the  two  shadows  of 
the  same  object  and  the  diameter  of 
the  free  part  of  one  of  the  circles  of 
diffiision  forms  a  ratio  that  is  equal  to 
that  between  the  distance  of  the  ob- 
ject from  the  retina  and  that  of  the 
pupil  from  the  retina. 

Let  A  and  B  be  two  luminous  points 
in  the  anterior  focal  plane  of  eyeball ; 
(9,  the  object ;  /,  the  center  of  pupil ;  s  and  s'  the  shadows  of  o,  cast 
by  A  and  B,  and  c  and  c'  the  centers  of  the  circles  of  diffusion. 
Since  A  and  B  are  at  the  anterior  focus  of  eye,  line  pc  is  parallel 
to  OS  and  pc'  parallel  to  os' .     A  cpc'  and  sos'  are  then  similar. 


ss' 


OS 

"pj 


Figure  2  shows :  cc'  =  DE=  R  (radius  of  circle)  +  a. 


200  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

To  take  these  measurements  we  look  at  a  piece  of  white  paper 
well  illumined,  through  two  stenopaic  openings,  and  notice  the  place 
where  the  shadows  are  projected  as  well  as  the  borders  of  the  circles 
(Donders).  Duncan  made  the  measurements  by  comparing  the  entop- 
tic  phenomenon  with  a  scale  viewed  by  the  other  eye.  If  the  object 
of  observation  is  more  or  less  transparent,  it  will  not  cast  a  definite 
shadow  but  being  more  or  less  refracting  than  the  surrounding 
medium,  will  look  brighter  in  the  center  or  on  the  edge.  If  the  body 
is  more  refracting  than  the  surrounding  medium  on  account  of  its 
shape,  or  having  a  different  index,  it  will  appear  lighter  in  the  center, 
while  if  less  refracting  the  image  will  be  dark  with  a  light  border. 
This  difference  of  refraction  is  well  marked  in  case  of  the  star-figure 
of  the  lens  in  people  with  incipient  cataracts  ;  in  some  the  striae  appear 
dark  and  in  others  light.  Another  phenomenon  due  to  the  influence 
of  the  light  that  passes  into  the  eye  through  the  sclera  is  observed 
when  we  place  ourselves  near  a  window,  so  that  one  eye  is  illumined 
while  the  other  one  is  in  the  shade.  After  a  while  it  will  be  noticed 
that  the  white  objects  seen  with  the  illuminated  eye  assume  a  green- 
ish tint,  while  they  appear  red  to  the  fellow  eye,  when  first  one  and 
then  the  other  eye  is  closed.  The  light  that  passes  through  the 
sclera  and  the  chorioid  is  colored  red  by  the  blood  in  the  latter  tunic, 
and  the  retina  becoming  fatigued  for  red  objects  appears  tinted  with 
the  complementary  color,  green  ;  the  other  eye  sees  red  by  contrast. 

When  we  read  in  sunlight  we  at  times  see  the  letters  colored 
vividly  red.  The  light  that  passes  through  the  membranes  of  the 
eyeball  is  added  to  that  which  passes  through  the  pupil.  It  is  not 
sufficiently  great  to  change  the  color  of  the  white  paper  illuminated 
by  the  sun,  but  does  change  the  color  of  the  black  letters  that 
contain  very  little  white  light. 

If  we  look  at  a  very  fine  luminous  point  we  see  it  surrounded  by  a 
number  of  fine  colored  radiations,  which  are  known  under  the  name 
of  ciliary  corona.  Its  extent  varies  with  the  intensity  of  the  light 
looked  at.  The  cause  of  this,  in  all  probability,  is  to  be  found  in  the 
fibrous  structure  of  the  crystalline  lens.      Besides  the  ciliary  corona 


ENTOPTIC    PHENOMENA.  20I 

most  folks  see  around  the  entire  luminous  source  a  vivid-colored  or 
diffraction  ring,  red  outside  and  blue  inside.  The  diameter  of  the 
ring  is  about  three  degrees.  A  larger  ring  appears  to  every  eye 
when  the  pupil  is  dilated,  as  pointed  out  by  Druault  &  Solomonsohn. 
It  presents  the  colors  in  the  same  order  as  the  smaller  ring.  Quite 
near  the  source  of  light  there  are  several  small  well-defined  black 
rings  to  be  seen,  due  to  diffraction  by  the  edge  of  the  pupil.  The 
smaller  colored  ring  is  probably  due  to  the  epithelium  of  the  cornea, 
and  is  analogous  to  the  rings  seen  when  we  look  through  a  piece  of 
glass  covered  with  a  thin  layer  of  lycopodium  powder,  Druault 
found  that  the  epithelium  on  the  anterior  surface  of  the  cornea  could 
be  removed  without  disturbing  the  colored  rings,  but  that  they  dis- 
appeared when  Descemet's  endothelium  was  interfered  with.  He 
observed  these  facts  by  looking  through  the  cornea  of  a  dead  eye. 
The  larger  colored  circle  seen  about  the  point  of  light  is  due  to  the 
fibrous  structure  of  the  crystalline  lens  acting  as  a  grating.  Druault 
also  produced  this  phenomenon  with  a  dead  crystalline  lens.  Glau- 
comatous patients  see  rings  of  a  similar  nature  but  they  are  larger, 
ten  to  eleven  degrees  in  diameter.  As  the  diameter  of  the  rings  are 
inversely  proportional  to  the  size  of  the  object  producing  them,  the 
glaucomatous  halo  must  be  produced  by  the  cells  of  the  endothelium 
which  are  much  smaller  than  the  cells  of  the  epithelium  of  the  cornea 
(Schiotz). 

Dr.  Tscherning  recently  described  a  sort  of  entoptic  phenomenon, 
which  is  observed  under  the  following  circumstances.  We  surround 
a  lamp  with  a  transparent  shade  made  of  some  layers  of  colored  tis- 
sue paper  for  example.  We  place  ourselves  at  a  few  meters'  distance 
and  interpose  an  opaque  screen,  in  which  there  is  made  a  vertical 
slit.  The  screen  should  be  at  about  30  cm.  in  front  of  the  eye. 
Keeping  the  left  eye  closed  we  fix  a  point  on  the  screen  near  the 
right  border  of  the  slit.  We  begin  by  holding  the  head  so  that  the 
eye  will  be  in  darkness,  and  then  move  the  head  so  that  the  eye 
enters  the  luminous  pencil  that  passes  through  the  slit,  while  main- 
taining fixation  at  the  same  spot.     Immediately  the  phenomenon  will 


202  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

be  seen  to  appear  under  the  form  of  two  arcs,  feebly  luminous  but 
bright,  going  from  the  slit  towards  the  blind  spot,  curving  about  the 
point  of  fixation.  The  arcs  soon  disappear  and  the  space  between 
them  becomes  filled  by  a  bluish  light,  and  then  the  whole  disappears 
to  reappear  on  the  least  motion  of  the  eyeball.  The  form  of  the  arc 
resembles  the  course  of  the  nerve  fibers  between  the  macula  and 
papilla,  and  its  appearance  resembles  that  of  phosphorescent  bodies, 
by  the  bluish  color  and  by  the  impression  that  it  gives  of  being  feeble 
and  bright  at  the  same  time. 


CHAPTER   XV 


MOVEMENTS    OF   THE    EYEBALLS 

The  eyeball  in  its  movements  simulates  very  closely  a  ball-and- 
socket  joint.  It  is  capable  of  being  moved  in  many  directions  by 
six  muscles  that  are  attached  to  it.  All  movements  of  the  eyeball 
take  place  about  a  point  in  the  vitreous  lying  about  1.7  mm.  poste- 
rior to  the  center  of  the  globe.  This  point  is  called  the  center  of 
rotation,  and  coincides  with  the  center  of  curvature  of  the  sclera, 
lying  10  mm.  anterior  to  its  posterior  surface. 

Donders  and  Dojer  determined  the  position  of  the  center  of  rota- 
tion in  the  following  manner :  They  first  measured  the  diameter  of 
the  cornea  by  means  of  the  ophthalmometer,  and  then  placed  a  hair 
stretched  vertically  across  a  ring 
in  front  of  the  cornea.  The  an- 
gular size  of  the  lateral  move- 
ments of  the  eyeball  needed  to 
bring  the  hair  successively  over 
the  inner  and  the  outer  edge 
of  the  cornea  was  measured. 

p  =  x  tangent  of  angle  A  CD, 
from  which  the  value  of  x  is  calculated.     Adding  to  this  value  the 
height  of  the  cornea,  we  find  the  distance  of  the  center  of  rotation 
from  the  vertex  of  the  cornea,  namely,  1 2  mm. 

Through  this  point  of  rotation  pass  three  lines  or  axes  about  which 
the  eyeball  makes  all  its  simple  movements.  The  primary  axes  are 
the  antero-posterior,  horizontal  and  vertical.  The  antero-posterior 
axis  joins  the  center  of  rotation  with  the  object  looked  at,  and  nearly 
coincides  with  the  visual  axis.  It  is  the  line  of  fixation.  About  this 
axis  the  eyeball  makes  its  rotary  movements  or  torsion,  as  it  is 
termed.     At  right  angles  to  this  line  and  joining  the  centers  of  rota- 

203 


204 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


tion  of  the  two  eyes,  is  the  horizontal  or  transverse  axis,  around 
which  the  movements  of  elevation  and  depression  take  place  (sur- 
sumduction,  or  -version,  and  deorsumduction  or  -version).  At  right 
anp-les  to  both  of  these  lines  is  the  vertical  axis  around  which  the 
eyeball  makes  its  lateral  movements,  that  is,  adduction,  towards  the 
nose,  and  abduction,  towards  the  temple. 

The  six  extra-ocular  muscles  can  be  divided  into  three  pairs,  each 
pair  having  a  common  axis  around  which  it  moves  or  rotates  the 
eyeball.  Only  the  common  axis  of  the  laterally-acting  muscles,  that 
of  the  internal  and  external  recti,  coincides  with  one  of  the  three 
axes  just  described,  that  is,  with  the  vertical  axis.  The  other  two 
pairs  of  muscles  have  their  own  axes  of  action  and  must  be  analyzed 
with  regard  to  all  three  ocular  axes,  each  of  the  four  muscles  pro- 
ducing elevation,  depression,  abduction  or  adduction.  The  superior 
and  inferior  recti  muscles  rotate  the  eyeball  around  an  axis  that 

passes  horizontally  through  the 
center  of  rotation  and  running 
posteriorly  cuts  the  median 
plane  of  the  body  at  an  angle 
of  about  70  degrees.  The  ob- 
liques rotate  the  eyeball  around 
a  horizontal  axis  that  passes 
through  the  center  of  rotation 
and  cuts  the  median  plane  of 
the  body  anterior  to  the  eyes,  at 
an  angle  of  about  35  degrees. 
Each  of  these  axes  is  at  right 
angles  to  the  direction  of  the 
insertion  of  their  respective 
muscles. 

A  reference  to  the  figure  will 
explain  the  axes  of  rotation  just 
described ;  the  vertical  axis  being 
at  right  angles  to  the  plane  of  the  paper,  cannot  be  shown  in  the  figure. 


MOVEMENTS   OF   THE   EYEBALLS. 


205 


The  continuous  lines  in  the  figure  drawn  as  diameters  represent 
the  primary  ocular  axes,  with  the  exception  of  the  vertical  one  ;  the 
dotted  lines  the  axes  of  rotation,  or  secondary  axes. 

Each  muscle  moves  the  eyeball  as  follows,  reference  being  had  to 
the  direction  that  the  cornea  is  made  to  face:  The  internal  rectus 
simply  draws  the  eyeball  in  towards  the  nose ;  the  external  rectus, 
outwards  towards  the  temple.  The  superior  rectus  turns  the  cornea 
upwards,  slightly  inwards,  and  twists  the  upper  end  of  the  vertical 
meridian  of  the  cornea  inwards,  the  eyeball  turning  upon  its  antero- 
posterior axis  (mesial  torsion).  The  inferior  rectus  moves  the  eye- 
ball downwards  and  inwards,  and  tilts  the  lower  end  of  the  vertical 
meridian  of  the  cornea  inwards,  throwing  the  upper  end  outwards 
(lateral  torsion).  In  regard  to  torsion  the  superior  and  inferior  recti 
oppose  each  other.  The  superior  oblique  turns  the  cornea  down- 
wards, outwards,  and  produces  mesial  torsion  ;  the  inferior  oblique 
directs  the  eyeball  upwards,  outwards,  and  produces  lateral  torsion. 
The  superior  recti  and  the  inferior  obliques,  and  the  inferior  recti 
and  superior  obliques  work  together  to  maintain  the  vertical  position 
of  the  vertical  meridian  of  the  cornea  in  vertical  movements  of  the 
eyeball.  The  table  gives  the  actions  of  the  extraocular  muscles  at  a 
glance. 

Adduction  by :  superior,  inferior  and  interior  recti.  The  adduct- 
ing  action  of  the  vertical  recti  increases  in  proportion  as  the  eyeball 
is  adducted. 

AbducUon :  exterior  recti  and  superior  and  inferior  obliques.  The 
abducting  action  of  the  obHques  increases  in  proportion  as  the  eye- 
ball is  abducted. 

Sursumduction :  superior  recti  and  inferior  obliques.  Deorsum- 
duction:  inferior  recti  and  superior  obliques.  Depression  and 
elevation  are  effected  mainly  by  the  obliques  when  the  eye  is  in 
adduction  and  by  the  recti  when  the  eye  is  in  abduction. 

Inwards  and  upwards:  interior  and  superior  recti  and  inferior 
obliques. 


206  THE   EYE.    ITS   REFRACTION   AND   DISEASES. 

Inwards  and  downwards :  interior  and  inferior  recti  and  superior 
obliques. 

Outwards  and  upwards:  exterior  and  superior  recti  and  inferior 
obliques. 

Outwards  and  downwards :  exterior  and  inferior  recti  and  superior 
obliques. 

While  this  table  is  theoretically  true,  it  is  probable  that  all  six 
extra-ocular  muscles  are  concerned  each  time  the  eyeball  makes  any 
movement.  The  axis  around  which  the  eyeball  turns  is  therefore 
always  different  from  the  three  described  above  (primary  axes),  and 
perhaps  no  ocular  movement  is  as  simple  as  would  be  indicated  from 
the  above  table.  When  the  two  eyes  have  their  visual  axes  parallel 
and  lying  in  the  horizontal  plane,  the  eyes  are  said  to  be  in  the  pri- 
mary position. 

The  primary  position  is  more  exactly  defined  as  that  from  which 
the  eyeball  can  make  both  vertical  and  horizontal  movements  with- 
out affecting  the  vertical  meridian  of  the  cornea. 

All  other  positions  of  the  eyeball  are  secondary.  Under  normal 
conditions  both  eyes  move  together  in  associate  or  conjugate  move- 
ments, of  which  there  are  three  forms,  as  follows :  Both  eyes  moving 
in  the  same  direction,  as  turning  to  the  right  (dextroversion),  to  the 
left  (sinistroversion),  turning  up  (bilateral  sursumversion),  or  down 
(bilateral  deorsumversion).  (2)  The  movement  of  convergence,  and 
(3)  the  movement  of  the  eyes  back  to  parallelism,  or  even  divergence 
as  in  certain  stereoscopic  exercises,  from  convergence.  There  are 
two  other  associated  muscular  movements  which  may  be  mentioned, 
namely,  that  between  the  superior  recti  and  the  obliques  in  prevent- 
ing torsion,  in  oblique  directions  of  the  gaze,  and  that  between  the 
sphincter  of  the  pupil  and  the  ciliary  muscle  in  accommodation.  The 
eyes  are  able  to  rotate  upwards  through  t,^  degrees  of  arc;  inwards, 
48 ;  downwards,  50 ;  outwards,  53  degrees,  according  to  Dr.  Stevens. 
According  to  Landolt,  the  eyeball  is  able  to  move  through  about  45 
degrees  of  arc  in  every  direction.  If  in  any  one  direction  the  excur- 
sion of  the  eyeball  is  less  than  30,  it  may  be  considered  pathological. 


MOVEMENTS   OF   THE   EYEBALLS. 


207 


The  field  of  fixation  is  not  by  any  means  a  fixed  quantity.  The  ex- 
cursions of  the  eyeball  are  obtained  most  accurately  by  using  Stevens' 
tropometer,  illustrated  and  explained  below. 

It  consists  essentially  of  a  telescope  in  which  the  inverted  image 
of  the  examined  eye  is  found  at  the  eyepiece,  where,  either  as  an 
aerial  image  or  as  an  image  upon  the  ground  glass,  its  movements 


can  be  accurately  observed.  A  graduated  scale  in  the  eyepiece 
permits  every  movement  of  rotation,  in  any  direction,  to  be  exactly 
measured. 

Description  of  the  Scale,  Fig.  B. — The  long  line  between  and  at 
right  angles  to  the  shorter  lines  divides  two  similarly  graduated 
scales  running  in  different  directions;  the  larger  circle  represents 
the  outer  border  of  the  cornea,  the  edges  of  which  are  in  contact 
with  the  two  strong  lines ;  the  interval  between  each  pair  of  short 
lines  of  the  scale  is  ten  degrees  of  arc,  commencing  at  the  strong 
line  in  each  case.     If  now  the  head  of  the  person  examined  is  held 


208 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


firmly  in  the  primary  position  and  the  eye  caused  to  rotate  strongly 
in  a  given  direction,  the  arc  through  which  the  border  of  the  cornea 
passes  may  be  accurately  read    upon   the   scale.     In  the  figure  B 

the  curved  dotted  line  repre- 
sents a  new  position  of  the 
border  of  the  cornea. 

Suppose  that  the  person  ex- 
amined has  been  directed  to 
look    strongly    upward,    then 
the  cornea  has   moved  down 
the  scale  and  reaches  the  point 
in  this  example  of  40°,  that 
being    the    measure    of    this 
rotation.      By  means   of   the 
small  lever  the  scale  can  be 
placed  horizontally,  vertically 
or  obliquely,    and   by  means 
of  the  two  graduations  meas- 
urements   in    opposite    direc- 
tions can  be  made. 
Directions  for  Use  of  Tropometer.  —  If  it  is  desired  to  determine 
the  upward  rotation  the  border  of  the  cornea  is  made  to  coincide 
with  the  strong  line  which  appears  in  the  upper  part  of  the  scale  at 
the  right  hand. 

The  adjustment  is  made  by  means  of  the  milled  head  at  the  side 
of  the  standard.  As  the  eye  rotates  up,  the  image  moves  down.  In 
determining  the  downward  rotation  the  strong  line  at  the  lower  left- 
hand  side  of  the  scale  is  taken  as  the  point  of  departure. 

For  lateral  rotation  the  scale  is  turned  to  the  horizontal  position 
and  the  corresponding  strong  lines  used  as  before. 

In  order  to  adjust  the  upper  border  of  the  cornea  on  the  line,  it 
will  generally  be  necessary  for  the  examiner  to  place  the  left  hand 
upon  the  forehead  of  the  patient  and  make  gentle  traction  of  the 
upper  eyelid  by  the  thumb.  This  application  of  the  hand  to  the 
forehead  is  advisable  in  all  measurements,  as  by  this  means  the 


MOVEMENTS    OF    THE    EYEBALLS.  209 

examiner  is  able  to  detect  even  a  slight  movement  of  the  head, 
which  would  vitiate  any  measure  of  the  rotation.  In  adjusting  the 
head  to  the  head-rest,  the  teeth  should  be  closed  and  the  line  of  the 
upper  lip  just  below  the  nose  should  be  in  a  vertical  line  below  the 
glabella  or  ridge  just  above  the  root  of  the  nose. 

The  eye  cannot  fix  the  same  point  for  even  a  little  while  without 
being  annoyed  by  the  formation  of  after-images  or  without  the  phe- 
nomenon of  Troxler  interfering.  The  eyes  are  therefore  in  perpetual 
motion  which  is  made  by  jerks.  They  fix  a  point,  make  a  movement ; 
fix  another  point,  and  so  forth.  During  reading  the  eyes  move  by 
jerks,  four  or  five  movements  for  a  line  of  an  ordinary  book,  and  a 
greater  movement  when  the  eye  is  shifted  from  one  line  to  another. 
Lamar  constructed  a  little  instrument,  that  he  supported  against  the 
upper  eyelid,  and  which  was  connected  with  the  ears  of  the  observer 
by  rubber  tubes.  Each  movement  of  the  eyeball  could  then  be  heard 
and  the  number  of  movements  easily  counted.  It  has  been  shown 
that  the  shorter  the  printed  line  within  certain  limits,  the  less  fatigu- 
ing is  it  upon  the  eyes. 

The  length  of  the  line  in  the  ordinary  newspaper  column  is  about 
the  length  that  fatigues  the  eyes  the  least.  It  is  impossible  to  cause 
a  movement  to  be  made  with  one  eye  without  the  other  one  moving 
also,  in  an  associated  movement.  The  following  simple  experiment 
however  would  seem  to  indicate  the  contrary.  Suppose  that  the  two 
eyes  are  fixing  a  point  a,  and  we  place  an  object  b  in  the  visual  line 
of  the  right  eye.  If  we  ask  the  person  to  fix  the  object  b,  the  left  eye 
is  directed  towards  this  point  while  the  right  eye  remains  apparently 
motionless.  But,  if  we  observe  closely  we  will  see  that  the  right  eye 
makes  really  two  slight  changes  of  position,  for  instead  of  receiving 
no  innervation,  as  one  would  think,  its  muscles  receive  two,  one  that 
would  cause  it  to  make  an  associated  movement  to  the  right  and 
another  that  would  cause  it  to  make  a  movement  of  convergence  to 
the  left ;  the  two  innervations  neutralize  each  other  so  that  the  eye- 
ball remains  apparently  motionless.  It  was  Hering  that  first  de- 
scribed this  experiment. 
14 


2IO  THE   EYE.    ITS   REFRACTION   AND    DISEASES. 

When  the  eyelids  are  closed,  especially  forcibly,  the  eyeballs  are 
rolled  up  and  out.  This  phenomenon  is  called  Bell's  phenomenon. 
It  was  until  recently  supposed  to  be  due  to  a  connection  between 
the  facial  and  the  oculo-motor  nerves,  but  histological  dissection 
does  not  warrant  any  such  supposition.  Lately  there  has  been  ad- 
vanced what  is  called  the  pressure-reflex  theory,  which  is :  That  the 
cornea  to  escape  the  pressure  of  the  stiff  tarsal  plate  of  the  lids, 
when  they  are  closed,  rolls  up  behind  the  softer  portions  of  the 
lids  in  obedience  to  a  reflex  started  in  the  fifth  nerves  of  the  cor- 
nea, and  carried  to  the  eye  muscles  through  the  third  nerve.  (Dur- 
ing sleep  the  pupils  are  contracted  and  possibly  the  ciliary  muscles 
also.) 

The  field  of  fixation  is  the  extent  of  space  in  which  the  eye  can 
successively  fix  an  object  that  is  gradually  moved  in  different  direc- 
tions before  it.  We  begin  by  placing  the  object  directly  in  front  of 
the  eyeball,  with  the  eye  in  the  primary  position,  and  move  the 
object  from  the  center  towards  the  periphery.  The  field  of  fixation 
is  conveniently  taken  upon  the  perimeter,  and  the  result  recorded 
upon  one  of  the  charts  used  for  recording  the  field  of  vision. 
The  extent  of  the  field  of  fixation  is  a  good  estimate  of  the  ability  on 
the  part  of  the  eye  to  rotate  in  different  directions.  '  The  extent  of 
the  field  taken  with  the  perimeter  should  coincide  with  the  results 
given  by  the  tropometer. 

To  take  the  field  of  fixation  the  patient  is  placed  as  for  taking  the 
field  of  vision.  Small  printed  matter  is  used  for  the  test  object. 
The  patient's  head  is  rendered  stationary  by  having  him  grasp  a 
wooden  bar  that  extends  cross-wise  in  front  of  the  chin  rest  between 
the  teeth,  or  the  hand  of  the  operator  may  be  placed  upon  the  head 
of  the  patient  so  as  to  perceive  any  motion  of  the  head.  The  fine 
printed  matter  is  then  moved  along  the  arc  of  the  instrument  from 
the  center  towards  the  periphery  and  the  patient  told  to  follow  it 
with  the  eye  (the  other  one  being  bandaged).  The  patient  continues 
to  turn  his  eye  as  the  print  moves  toward  the  periphery  and  the 
moment  when  he  has  turned  his  eye  in  that  direction  to  the  utmost 


MOVEMENTS   OF   THE   EYEBALLS. 


211 


the  print  passes  out  of  view,  that  is,  it  becomes  illegible  as  the  macula 
can  no  longer  be  brought  to  bear  upon  it. 

The  furthest  point  at  which  the  patient  is  able  to  read  the  print 
without  moving  the  head  expresses  the  limit  of  rotation  of  the  eye- 
ball in  that  direction.  This  is  done  for  different  meridians  and  the 
points  on  the  chart  thus  obtained  connected  by  a  straight  or  curved 
line.  If  the  vision  is  too  poor  to 
take  the  field  of  fixation  with 
printed  matter  a  lighted  taper 
may  be  used  as  the  object  of  fix- 
ation. As  it  is  moved  along  the 
arc  the  eye  follows  it. 

When  the  eyeball  has  rotated 
in  any  one  direction  to  its  fullest 
extent  the  catoptric  image  of  the 
candle  from  the  cornea  becomes 
eccentric,  no  longer  seen  at  the 
center  of  the  cornea,  as  it  was  so 
long  as  the  eye  was  directed  at 
the  light. 

In  the  figure,  t,  t'  and  t"  rep- 
resent three  positions  of  the  test 
object  along  the  perimetric  arc. 
As  the  object  is  moved  from  /  to  t\  the  cornea  is  depressed,  causing 
the  macula  to  ascend  from  m  to  ni\  so  that  the  image  of  /'  still  falls 
upon  it,  but  when  the  object  reaches  the  point  /"  the  eyeball  can  no 
longer  follow  it,  so  the  image  of  H'  now  falls  off  of  the  macula  and 
the  print  of  the  test  object  is  no  longer  legible. 

A  rough  but  sufficiently  accurate  test  of  the  motility  of  the  eyeball 
for  practical  purposes  is  to  have  the  patient  follow  with  the  eyes  the 
finger  of  the  observer  as  it  is  moved  about  in  front  of  them.  One 
should  notice  whether  both  eyes  move  together,  and  whether  in 
elevation  and  depression  of  the  eyeballs,  the  lids  accompany  the 
excursions  of  the  latter. 


212  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

In  lateral  movements  of  the  eyeball,  that  is,  adduction  and  in 
abduction,  linear  mensuration  of  the  excursions  of  the  eyeball  is 
applicable.  The  patient  is  first  made  to  look  straight  ahead  at  an 
object  at  a  distance  of  twenty  feet  in  the  horizontal  plane  with  the 
eyes  and  in  the  median  line  of  the  face.  An  ink  dot  is  then  made 
upon  the  lower  lid  below  the  outer  edge  of  the  cornea  (with  the  eye- 
ball in  this  primary  position),  and  below  the  outer  angle  of  the  lids, 
and  the  distance  between  them  measured  (distance  bd  in  the  figure 
below).  The  eye  then  looks  out  to  its  fullest  extent  and  a  dot  is 
then  made  below  the  outer  edge  of  the  cornea  in  the  new  position 
of  the  eyeball  as  before  (distance  cd  in  the  figure).  The  patient 
next  looks  in  towards  the  nose  as  far  as  possible,  and  another  dot 

made  on  the  lower  lid  below  the  outer  edge 
of  the  cornea  (distance  ad  in  the  figure). 

Suppose  that  the  first  value  is  8  mm., 
ana  the  second  one  i  mm.,  then  the 
amount  of  abduction  equals  7  mm.  Sup- 
pose that  the  distance  from  the  outer  edge 
of  the  cornea  to  the  outer  angle  of  the 
eye,  when  the  eye  is  adducted  is  18  mm., 
the  amount  of  adduction  is  then  10  mm.  The  measurement  of  the 
excursions  of  the  eyeball  is  important  in  order  to  determine  the  de- 
gree of  paralysis  of  extra-ocular  muscles,  and  the  effect  of  treatment ; 
the  prognosis  of  squint  operations  and  so  on. 

The  binocular  field  of  fixation,  or  the  extent  of  space  in  which 
there  is  single  binocular  fixation,  is  called  the  horopter  or,  as  Dr. 
Savage  suggests,  the  monoscopter  (ju,ovo5,  single;  cr/coTrewi',  seeing). 
The  monoscopter  occupies  different  planes  and  is  a  surface  of  revo- 
lution formed  by  revolving  a  circular  plane  upon  its  chord,  a  line 
joining  the  centers  of  rotation  of  the  two  eyes. 

The  limits  of  the  monoscopter  in  all  directions  is  not  less  than 
thirty-three  degrees.  If  binocular  diplopia  occurs  uniformly  when 
the  eyes  have  been  carried  less  than  thirty  degrees  from  the  primary 
position,  it  is  distinctly  pathological.     By  reference  to  the  cut  it  will 


MOVEMENTS    OF   THE    EYEBALLS. 


213 


be  seen  that  the  three  points  chosen  for  the  construction  of  the  circle 

are:  b,  the  point  of  fixation  of  the  two  eyes;  c  and  c\  the  centers  of 

retinal  curvature  of  the  left  and  right  eye  respectively.     The  line  of 

single  vision  is  in  the  plane  of 

the  visual  axis.     Points  situated 

anywhere  on  this  line  capable  of 

sending  light  into  the  two  eyes, 

will  be  seen  singly  by  them.   Such 

are  the  points  a  and  d,  the  furthest 

points  in  the  extreme  periphery 

that  can  send  light  to  the   two 

eyes,  and  therefore  can  be  seen 

singly.      The      monoscopter     is 

formed  by  the  revolution  of  the 

circular    plane    {abed)    upon   its 

chord  cc'.     Such  a  surface  is  a 

combination  of  a  concave  sphere  and  a  concave  cylinder  (a  section 

of  a  concave  tore).     All  angles  formed  between  the  visual  lines  in 

the  monoscopter  are  equal  to  each   other,  therefore   there   is   the 

same  inclination  of  the  visual  lines  to  each  other  throughout  the 

surface. 


CHAPTER   XVI 

THE    LAW    OF    LISTING 

Each  time  that  the  look  returns  to  the  same  point,  the  eye  reas- 
sumes  the  same  position  (Bonders).  If  we  gaze  upon  a  colored  rib- 
bon (red  for  instance),  stretched  horizontally,  long  enough  to  give 
rise  to  an  after-image,  and  then  project  the  latter  upon  the  wall, 
keeping  the  head  motionless,  the  projected  after-image  assumes  the 
same  position  each  time  that  particular  spot  is  fixed,  although  not 
always  horizontal.  This  position  is  determined  by  the  law  of  Listing, 
according  to  which  law  the  eye  may  be  brought  from  the  primary  to 
any  secondary  position  by  a  rotation  around  an  axis  that  is  perpen- 
dicular to  the  two  successive  directions  of  the  visual  line.  Or  in 
other  words,  as  the  eye  passes  from  the  primary  to  a  secondary  posi- 
tion, the  angle  of  torsion  of  the  eye  is  the  same  in  the  secondary 
position  as  if  the  eye  had  rotated  about  a  line  perpendicular  to  the 
first  and  second  positions  of  the  line  of  fixation. 

The  axes  of  Listing  are  all  contained  in  a  plane  that  is  perpendicu- 
lar to  the  primary  position  and  pass  through  the  center  of  rotation 
of  the  eyeball.  This  plane  is  invariably  connected  with  the  head 
as  the  primary  position  is  that,  when  the  eyes  are  directed  straight 
ahead,  giving  to  the  head  the  position  that  seems  most  natural.  It 
may  be  necessary  for  the  individual  to  lean  the  head  a  little  backward 
or  forward  in  order  to  make  the  primary  position  horizontal.  To 
demonstrate  the  law  of  Listing  we  place  ourselves  at  a  distance  of 
one  or  two  meters  from  the  wall  upon  which  is  placed  a  fixation 
mark  on  level  with  the  eyes.  The  position  of  the  head  is  rendered 
secure.  A  rectangular  cross  is  placed  upon  the  wall  with  its  arms 
horizontal  and  vertical.  The  cross  is  made  to  contrast  with  the  color 
of  the  wall  so  that  a  plain  after-image  can  be  obtained  after  gazing  at 
it  for  a  while.     We  then  move  the  head  a  little  forward  or  backward 

214 


THE    LAW   OF    LISTING. 


21 


or  to  the  one  side  or  the  other,  until  a  position  is  obtained  that  on 
moving  the  look  along  the  prolongation  of  each  of  the  arms  of  the 
cross,  the  after-image  of  this  arm  glides  all  the  time  along  itself  We 
observe  that  there  exists  only  one  position  of  the  head  in  which  this 
is  possible.  In  every  other  position  of  the  head  the  after-image  of 
the  cross  turns  partially  around  during  the  displacement  of  the  look. 

Suppose  that  we  fix  a  point  to  the  side  of  the  cross  on  the  same 
horizontal  line.  Since  the  meridian  that  was  horizontal  when  fixing 
A  is  also  horizontal  when  fixing  B,  it  is  clear  that  the  look  may  be 
brought  from  A  to  B,  by  a  motion  around  a  vertical  axis,  that  is 
around  an  axis  that  is  perpendicular  to  the  two  positions  of  the  visual 
line.  It  is  the  same  tor  displacement  in  the  vertical  direction ;  to 
prove  that  it  is  true  likewise  for  oblique  displacements  of  the  gaze 
we  tilt  the  cross. 

It  is  then  easy  to  prove  that  the  after-image  of  one  of  the  arms  of 
the  cross  glides  all  the  time  along  its  prolongation,  when  the  look 
follows  this  prolongation,  and  that  the  eye  in  consequence  turns 
around  an  axis  perpendicular  to  this  meridian,  and  thus  the  law  of 
Listing  is  verified.     In  fixing  the  point  C,  figure  i ,  we  notice  that  the 


11 


+--1- \ 

I  I 

*  • 

I  >  I 

>-— J---4. 


!K;-— X- — :?^"= 


%--^--¥ 


X-'- — -% -X 


vertical  arm  in  the  cross  of  the  after-image  is  no  longer  vertical ;  it 
has  undergone  a  rotation,  the  upper  extremity  has  gone  to  the  right. 
This  fact  is  simply  in  consequence  of  the  law  of  Listing.  The  me- 
ridian that  was  vertical  when  fixing  A  cannot  remain  vertical  when 
the  eye  turns  around  an  axis  that  is  at  right  angles  to  the  direction 
AC.     In  Fig.  2  the  cross  is  tilted  to  show  better  how  the  after-image 


2l6  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

glides  along  the  prolongation  of  its  arms.  Donders  attributed  this 
phenomenon  to  a  rotary  movement  of  the  eyeball  around  the  visual 
axis.  The  displacement  of  the  horizontal  arm  of  the  cross  in  the  con- 
trary direction  is  due  to  the  fact  that  the  projection  of  the  after-image 
is  upon  a  plane  not  perpendicular  to  the  visual  line.  If  we  project 
the  image  upon  the  concave  surface  of  a  hollow  hemisphere,  at  the 
center  of  which  is  placed  the  eye,  the  cross  seems  to  have  under- 
gone a  complete  rotation  to  the.  right.  In  these  experiments  the 
position  of  the  two  eyes  is  exactly  the  same :  we  can  cover  one  eye 
or  the  other  without  changing  the  position  of  the  after-image. 

The  law  of  Listing  merely  defines  the  position  of  the  eye  in  repose 
and  it  is  probable  that  the  eyeball  never  makes  a  movement  about 
the  axes  of  Listing,  nor  that  the  eyeball  always  follows  the  same  path 
in  passing  from  one  point  to  another.  As  Tscherning  suggests,  the 
best  way  probably  to  study  the  manner  of  movements  of  the  eye 
would  be  to  quickly  bring  the  look  from  one  point  to  another,  leav- 
ing the  eye  all  the  while  exposed  to  a  rather  intense  light.  The 
after-image  would  then  be  in  the  form  of  a  line  that  permits  some 
conclusion  to  be  drawn  in  regard  to  the  direction  of  the  movement 
of  the  eye.  Meissner's  method  seems  to  verify  the  law  of  Listing 
in  a  very  exact  manner,  as  follows :  If  we  hold  a  plumb  line  in  front 
of  the  wall  and  fix  an  object  nearer  to  the  eyes  than  the  line,  we 
see  the  latter  in  double  images  (homonymous).  We  should  expect 
to  see  two  parallel  vertical  lines,  but  the  two  lines  seen  converge 
above.  If  we  fix  a  point  behind  the  line,  the  line  again  appears 
double  but  the  two  diverge  above.  If  we  look  at  a  rectangular  cross, 
its  arms  being  vertical  and  horizontal  with  the  right  eye  the  upper 
right  and  lower  left  angles  appear  larger  than  the  other  two  angles 
while  the  reverse  takes  place  for  the  left  eye.  Since  to  the  right  eye 
a  vertical  line  appears  to  slant  to  the  left  there  must  be  a  leaning  to 
the  right  of  the  vertical  meridian  of  the  retina  that  seems  vertical. 
The  direction  of  this  line  may  be  determined  in  the  following  manner : 
Upon  a  circular  piece  of  cardboard  draw  a  diameter ;  place  the  disc 
upon  a  vertical  wall ;  now  let  the  observer  try  to  turn  the  disc  so 


THE    LAW   OF    LISTING. 


217 


that  the  diameter  will  be  vertical,  using  one  eye  at  a  time.  With 
the  right  eye  the  upper  extremity  of  the  line  will  be  placed  several 
degrees  too  far  to  the  right,  and  with  the  left  eye  too  far  to  the 
left. 

This  fact  will  be  observed  if  a  plumb  line  be  held  so  that  it  will 
pass  through  the  center  of  the  disc.  Another  method  of  determin- 
ing the  angle  formed  between  the  apparently  vertical  diameters  cf 
the  retinse  is  that  of  Volkmann.  Place  upon  the  wall  two  small  discs, 
so  that  the  distance  between  their  centers  will  be  equal  to  the  dis- 
tance between  the  pupils  of  the  observer.  Upon  each  disc  is  to  be 
drawn  a  radius.  The  right  eye  now  observes  the  right-hand  disc  and 
vice  versa.  The  same  experiment  may  be  performed  by  using  the 
stereoscope,  as  suggested  by  Javal.  One  of  the  radii  is  placed  ver- 
tically and  an  attempt  made  to  place  the  other  one  so  that  the  two 
will  form  a  single  continuous  straight  line.  It  will  be  found  that  it  is 
necessary  that  the  lines  should  form  an  angle  of  about  two  degrees, 
in  order  that  they  may  appear  straight.  There  is  a  slight  difference 
in  the  direction  of  the  apparent  and  the  real  horizontal  meridians  of 
the  two  retinas  as  well,  but  to  a  much  less  degree.  It  is  probable 
that  these  phenomena  are  due  to  the  more  important  part  played  by 
the  downward  look  in  our  every-day  life,  as  when  reading,  walking, 
etc.  If,  while  performing  the  experiment  of  Meissner,  we  draw  the 
lower  extremity  of  the  plumb  line  towards  us,  we  observe  that  the 
lines  become  parallel  when  the  plumb  line  has  a  position  at  right 
angles  to  the  visual  lines. 

Volkmann  found  that  each  eye  in  converging  for  a  distance  of  30 
cm.  made  a  rotatory  movement  of  one  degree  (mesial  torsion),  which 
it  would  not  have  made  if  the  visual  lines  were  parallel  in  taking  the 
same  position,  so  that  the  law  of  Listing  does  not  hold  when  the 
visual  lines  are  not  parallel.  Place  two  candles  one  meter  from 
each  other,  and  look  at  them  from  a  distance  of  one  or  two  meters, 
o-etting  the  eyes  as  nearly  in  the  primary  position  as  possible.  We 
then  try  to  converge  as  if  to  fuse  the  candles.  We  then  observe 
that  the  candles  appear  slightly  inclined  towards  each  other.     The 


2l8  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

inclination  increases  as  we  approach  the  candles  towards  each  other 
and  may  reach  as  much  as  fifteen  degrees. 

Heuck  taught  that  the  eyeball  underwent  a  rotation  around  the 
visual  axes  when  the  head  was  inclined  to  the  one  side  or  the  other, 
in  order  that  the  vertical  meridians  of  the  retinas  may  always  remain 
vertical.     This  rotatory  motion  does  exist  but  to  a  slight  extent,  as 
Javal  showed.     If,  however,  no  rotation  took  place  around  the  line 
of  vision  when  the  head  was  inclined  to  the  one  side  or  the  other, 
the  axes  of  astigmatic  spectacles  would  continue  to  coincide  with  the 
axes  of  the  wearer's  astigmatism,  but  this  is  not  the  case,  as  any 
one  wearing  astigmatic  spectacles  may  demonstrate.    With  the  head 
erect  all  the  lines  on  the  astigmatic  dial  may  appear  alike,  but  will 
appear  unequal  if  the  head  is  tilted  to  one  side  or  the  other.     Dr. 
Stevens  has  lately  devised  an   instrument   that  he  calls   the  clino- 
scope,  designed  to  further  the  study  of  the  declinations  of  the  ver- 
tical  meridians  of  the   retinae,   and   to   make  more   accurate  such 
studies  as  well  as  to  measure  with  a  degree  of  certainty  the  extent 
of  torsion  that  the  eyeball  undergoes  in  various  movements.     See 
the  following  cut  and  the  explanation : 


Stevens'  Clinoscope. 


The  clinoscope  consists  of  two  cylindrical  tubes,  each  about  three 
centimeters  in  diameter  and  fifty  centimeters  in  length.  The  tubes 
are  mounted  on  a  brass  platform,  which  holds  them  firmly  in  the  same 


THE    LAW   OF    LISTING.  219 

horizontal  plane,  at  a  distance  of  6.5  centimeters  between  the  centers 
at  a  fixed  point.  The  attachment  to  the  platform  permits  the  tubes 
to  be  adjusted  in  parallelism,  in  convergence  or  in  divergence  in  the 
plane  of  the  platform.  The  platform  is  attached  by  a  movable  joint 
to  the  upright  standard,  so  that  the  instrument  may  be  given  any 
desired  dip  ;  a  scale  and  pointer  indicate,  as  in  the  case  of  the 
clinometer,  the  dip  with  respect  to  the  horizon. 

The  tubes  are  caused  to  rotate  upon  their  longitudinal  axes  by 
means  of  thumb  screws,  as  seen  in  the  figure,  and  the  pointer  and 
scale  above  the  tubes  mark  the  rotation  with  accuracy. 

At  the  proximal  end  of  each  tube  is  a  clip,  in  which,  if  desired,  the 
observer  may  insert  a  glass  for  the  correction  of  his  refraction  or  any 
glass  from  the  trial  case.  At  the  distal  end  is  another  clip  and  pro- 
vision for  maintaining  precise  position  of  the  diagrams  to  be  used  in 
the  investigation.  These  diagrams  are  haploscopic  figures,  calculated 
to  aid  in  the  various  experiments  which  may  be  made.  These  may 
be  varied  according  to  the  wish  of  the  investigator.     Below  are  repre- 


sented three  pairs  of  these  diagrams.  Figure  i  represents  two  pins, 
one  to  be  seen  by  each  eye.  As  the  trained  observer  looks  into  the 
tubes,  the  two  tubes  and  the  two  pins  blend  as  one,  and  the  head  of 
the  long  pin  now  appears  in  the  middle.  An  adjustment  of  the  tubes 
by  rotation  on  the  long  axis  will  show  the  true  direction  of  the  merid- 
ian, vertical  or  horizontal,  according  to  the  position  of  the  diagrams, 
of  each  eye  upon  the  scale  above  the  tubes.  For  one  who  desires  to 
test  the  accuracy  of  Helmholtz's  theory  of  the  leaning  of  the  vertical 
meridian  upward  and  outward,  while  the  horizontal  meridian  remains 


220 


THE   EYE,   ITS   REFRACTION   AND    DISEASES. 


practically  horizontal,  Helmholtz's  diagram  (figure  2),  familiar  to  stu- 
dents of  physiological  optics,  may  be  used.     The  engraver  has  rep- 


_ 


E.B.MEYROWITZ.N.Y. 

Fig.  2. 


resented  these  diagrams  as  quadrilateral.     They  are  in  fact  circular, 
like  those  of  figure  i . 

For  testing  the  ability  of  the  eyes  to  rotate  upon  the  antero-pos- 
terior  axis  (torsion),  a  straight  line  running  across  each  disc  (figure  3) 


is  the  most  useful  figure.  The  lines  may  be  placed  vertically  or 
horizontally.  It  will  be  found  that  the  rotating  ability  is  much 
greater  when  the  lines  are  vertical. 

The  clinoscope  is  primarily  an  instrument  for  physiological  re- 
search, but  as  a  practical  instrument  it  has  been  found  of  much  value 
in  determining  the  declination  of  the  meridians  in  paralysis  of  the 
eye  muscles,  and  in  anomalous  adjustments  of  the  eyes  in  respect  to 
the  horizontal  visual  plane,  and  those  who  may  be  interested  in  de- 
termining the  power  of  torsion,  or  who  hope  to  increase  the  torsional 
ability  by  exercise,  will  find  the  clinoscope  a  correct  measure  in  the 
first  case,  and  an  efficient  aid  in  the  second.     The  instrument,  as 


THE   LAW   OF    LISTING.  221 

now  constructed,  is  mounted  on  a  base  similar  to  the  tropometer, 
with  a  head  piece,  which  permits  the  easy  and  perfect  adjustment  of 
the  patient  to  the  desired  position. 

Dr.  Savage  questions  the  truth  of  Listing's  law  and  brings  the 
following  arguments  to  bear  in  support  of  his  unbelief  That  the 
threatened  torsion  in  rotations  of  the  eyeball  in  oblique  directions 
does  not  occur,  being  prevented  by  action  of  the  obHques,  is  evident 
from  the  following  experiment.  Says  he :  An  astigmatic  with  his  cor- 
recting cylinders  may  be  asked  to  look  at  an  object  up  and  to  the 
right  at  the  maximum  obliquity.  If  torsion  has  occurred,  revolving 
the  axes  of  the  cylinders  in  the  direction  taken  by  the  best  meridian 
would  improve  the  vision,  while  as  a  matter  of  fact  it  renders  the 
vision  worse. 

Again  there  are  persons  who  have  small  corneal  scars  or  marks 
upon  the  iris  near  the  horizontal  meridian,  in  whom  we  should  be 
able  to  detect  torsion  of  the  eyeball  as  they  look  up  and  to  one  side. 
In  fact  these  marks,  if  in  the  horizontal  meridian  at  the  beginning, 
remain  so  no  matter  what  be  the  direction  of  the  gaze.  If  physio- 
logical torsion  did  take  place  we  would  be  deprived  under  certain 
conditions  of  the  power  to  judge  of  verticality  and  horizontality.  If 
the  obliques  did  not  prevent  torsioning  when  we  looked  up  and  to 
the  right  or  down  and  to  the  left  45  degrees,  we  would  see  a  vertical 
line  inclining  9°  44'.  An  oblique  position  of  the  eyes  does  not 
deprive  us  of  the  idea  of  verticality,  as  Savage  shows  our  idea  of 
verticality  depends  upon  the  fact  that  the  vertical  axes  of  the  eyes 
are  parallel  with  the  vertical  plane  of  the  head.  The  greatest  argu- 
ment in  favor  of  Listing's  law  is  the  experiment  of  after-images 
described  upon  a  foregoing  page. 

Such  leaning  of  after-images  as  shown  would  be  expected,  for  the 
stimulus  of  an  after-image  is  not  great  enough  to  call  into  full  action 
the  fifth  conjugate  innervation,  or  that  between  the  recti  and  the 
obHques.  In  passing  to  an  oblique  secondary  position  then  accord- 
ing to  many  the  eye  revolves  first  about  the  vertical  axis  and  then 
about  the  horizontal  axis. 


222 


THE   EYE,  ITS    REFRACTION   AND    DISEASES. 


The  following  table  is  taken  from  Savage,  which  is  equivalent  to  that 
of  Maddox.  It  expresses  the  value  of  torsion,  when  the  inclination  of 
the  axis  is  45  °,  for  various  degrees  of  rotation  if  the  obliques  did  not  act. 


Angle  of  Rotation 

5° 

10° 

15° 

20° 

25° 

30° 

35° 

40° 

45° 

Torsion 

f^Vz' 

26' 

1° 

14°  7' 

24°  9^ 

4°  6'     <^°  A.O' 

7°  33' 

9°  44' 

The  use  of  the  Maddox  rod  for  testing  the  ability  of  the  eyeball 
to  undergo  torsional  movements  was  first  pointed  out  by  Maddox 
himself,  but  has  been  used  by  very  few  for  this  purpose.  The  Mad- 
dox rod  is  admirably  adapted  for  determining  the  degree  of  torsion 
in  cases  of  paralysis  of  the  vertically  acting  muscles  of  the  eyeballs. 
It  also  serves  to  determine  in  any  given  case  whether  lines  are  truly 
vertical  and  horizontal  or  not,  or  whether  two  intersecting  lines  are 
at  right  angles  to  each  other  or  not,  and  we  can  ascertain  how  far 
these  estimates  are  affected  by  the  application  of  glasses. 

If  the  notions  of  the  patient  in  regard  to  the  direction  and  relations 
of  horizontal  lines  are  much  affected  by  glasses  we  may  expect  that 
they  will  cause  for  a  while  at  least  some  amount  of  annoying  distor- 
tion in  objects  seen  through  them.  Cylindrical  lenses  frequently 
produce  such  distortion,  even  when  the  lenses  are  othefwise  satisfac- 
tory. In  order  that  the  rod  of  Maddox  may  be  readily  applied  to 
the  solution  of  these  problems  Duane  has  constructed  an  instrument 
which  he  called  a  clinometer.  It  consists  of  two  multiple  Maddox 
rods  mounted  so  as  to  revolve  freely  in  a  frame.  Each  frame  is  pro- 
vided with  a  spring  catch  and  is  made  to  slide  along  the  horizontal 
arm  of  the  Stevens  phorometer.  The  rod  for  the  left  eye  has  a  ruby 
glass  backing  to  distinguish  the  images  as  seen  by  the  two  eyes. 
The  sides  of  the  frames  away  from  the  patient's  eyes  bear  a  gradu- 
ated arc  and  two  indices,  so  that  when  the  index  marked  V  is  at  O, 
and  the  arm  of  the  phorometer  perfectly  horizontal,  the  line  of  light 
seen  through  the  rod  is  perfecdy  vertical,  and  when  the  index  H  is 
at  O,  the  light  is  horizontal.  The  rods  are  revolved  by  means  of  two 
small  handles. 


THE    LAW    OF    LISTING.  223 

The  patient  is  seated  so  as  to  face  a  small  but  brilliant  light  on  the 
other  side  of  the  room  at  a  distance  of  about  twenty  feet,  the  room 
being  perfectly  dark.  The  patient  is  then  directed  to  look  at  the 
light  with  the  right  eye  through  the  right  Maddox  rod  and  the  latter 
rotated  until  he  says  that  the  streak  of  light  seen  through  it  is  per- 
fectly vertical.  The  other  eye  should  be  screened.  If  when  the 
patient  declares  the  line  to  be  vertical  the  index  stands  at  zero  or 
very  near  to  it  we  know  that  his  vertical  meridian  is  truly  vertical,  or 
on  the  contrary  if  he  should  say  the  line  is  vertical  when  the  index 
points,  a  number  of  degrees  to  the  one  side  or  the  other  of  the  zero 
mark  we  know  that  his  vertical  meridian  is  rotated  that  amount  to 
the  right  or  to  the  left  as  the  case  may  be. 

The  test  is  now  repeated  with  the  left  eye  alone,  the  right  one  being 
covered,  and  finally  with  both  eyes  open,  and  the  rods  turned  until 
the  two  lines  of  light  are  coincident  or  at  least  parallel.  The  same 
test  is  now  made  for  horizontal  lines.  To  estimate  the  accuracy  with 
which  the  patient  estimates  right  angles  we  turn  one  rod  so  that  the 
streak  is  vertical  and  the  other  one  so  that  the  streak  is  horizontal, 
the  true  amount  of  deviation  from  the  vertical  or  the  horizontal  to 
make  the  lines  appear  at  right  angles  being  read  from  the  graduation. 
The  eyes  should  occupy  as  nearly  the  primary  position  as  possible 
during  the  test.  The  instrument  shows  that  judgments  are  on  a 
whole  as  accurate  for  horizontal  lines  as  for  vertical  ones,  and  this 
about  equal  in  the  two  eyes. 

To  measure  the  torsional  ability,  each  rod  with  its  line  of  light  ver- 
tical is  placed  before  its  respective  eye.  The  patient  then  sees  a 
blended  red  and  white  line.  One  rod  is  then  rotated  until  he  just 
begins  to  see  the  lines  diverge.  The  amount  of  rotation  of  the  rod 
read  from  the  scale  then  indicates  the  ability  of  the  eyes  to  undergo 
torsion. 


CHAPTER   XVII 

NORMAL  AND  ABNORMAL  REFRACTION 

By  normal  refraction  we  mean  emmetropia,  or  the  condition  in 
which  the  retina  Hes  at  the  principal  focus  of  the  dioptric  system  of 
the  eyeball.  Such  an  eye  when  at  rest  or  in  repose  is  focused  for 
distant  objects  that  send  to  it  parallel  rays  (plane  waves)  of  light. 
Any  departure  from  this  ideal  constitutes  an  error  of  refraction,  or 
ametropia,  of  which  there  are  three  varieties,  namely,  hyperopia, 
myopia  and  astigmatism.  Presbyopia,  or  the  failure  of  accommoda- 
tion incident  to  age,  is  not  included  as  it  is  a  physiological  condition 
that  comes  to  all  eyes,  emmetropic  and  ametropic  alike,  and  is  not 
concerned  with  the  focusing  of  the  eye  for  distant  objects,  or  the 
focusing  of  parallel  rays  of  light.  Errors  of  refraction  lead  to  imper- 
fect vision  or  eye-strain  or  to  both.  If  the  error  is  small  it  may  be 
overcome  by  muscular  effort  on  the  part  of  the  eyeball  (if  it  is  of  such 
a  nature  that  accommodation  can  correct  the  error),  while  if  the 
defect  is  great,  effort  on  the  part  of  the  eye  being  of  no  avail,  eye- 
strain does  not  so  readily  ensue,  as  the  eyes  seem  to  discover  the 
uselessness  of  the  task  and  make  no  attempt  to  correct  the  trouble 
through  muscular  strain.  On  the  other  hand,  part  of  an  error  may 
be  overcome,  while  beyond  this  some  remains  to  render  the  vision 
indistinct.  Emmetropia  is  rarely  found,  although  it  is  the  ideal  con- 
dition or  state  of  refraction.  The  deviations  of  the  eyeball  from  the 
normal  are  insignificant  as  compared  with  the  deviations  of  other 
portions  of  the  body,  but  sufficient  to  cause  error  and  consequent 
inconvenience  to  many. 

Eye-strain  results  from  the  efforts  of  the  eye  to  prevent  indistinctness 
of  vision.  It  may  be  present  in  normal  eyes  working  under  unfavor- 
able conditions,  through  poor  illumination,  or  what  not,  or  by  excessive 
use.     It  may  be  caused  by  the  excessive  use  of  accommodation  from 

224 


NORMAL  AND  ABNORMAL  REFRACTION.  225 

looking  at  too  small  objects  or  caused  by  hyperopia  or  astigmatism. 
It  may  also  result  from  strain  put  upon  the  extra-ocular  muscles,  as 
from  strain  of  convergence  from  viewing  near  work  at  too  close  a 
range.  Strain  may  result  from  an  effort  to  keep  the  eyes  properly 
directed,  as  when  the  normal  relation  between  the  accommodation 
and  the  convergence  is  disturbed,  as  is  caused  by  hyperopia  or  by 
myopia,  or  by  lack  of  balance  between  opposing  extra-ocular  mus- 
cles (muscular  inefficiency).  In  such  cases  the  pain  felt  in  and  about 
the  eyeball  is  due  to  a  muscular  fatigue  to  the  greatest  extent,  also 
to  the  exhaustion  of  the  nerve  centers  in  the  effort  to  overcome  the 
error  or  to  appreciate  and  properly  interpret  the  blurred  retinal  pic- 
tures. The  ciliary  muscle  cannot  in  itself  give  rise  to  an  ache  or 
pain  due  to  fatigue  as  it  is  an  unstriped  muscle  and  such  do  not  have 
any  high  degree  of  irritability  (sensibility),  but  strain  from  excessive 
accommodation  gives  rise  to  reflex  pain  which  radiates  in  different 
directions  along  the  branches  of  the  fifth  nerve. 

Eye-strain  is  more  manifest  when  the  health  of  the  individual  is 
below  par,  and  is  frequently  unnoticed  until  during  convalescence 
from  an  exhausting  disease.  Eye-strain  makes  itself  evident  through 
various  affections  of  the  eye,  such  as  relaxation  of  accommodation, 
with  the  consequent  blurring  of  the  reading  matter  during  near 
work,  or  by  spasm  of  the  ciliary  muscle  causing  the  eye  to  be  ren- 
dered myopic  with  consequent  blurring  of  distant  seeing  especially. 
It  occasions  inflammations  of  the  lids,  cornea  and  conjunctiva,  and 
less  frequently  changes  in  the  chorioid  and  retina,  as  well  as  in  the 
crystalline  lens.  Opacities  of  the  lens  and  vitreous  body  are  at 
times  caused  by  eye-strain.  At  times  it  manifests  itself  in  the  de- 
crease of  hyperopia  or  in  the  increase  of  myopia,  if  the  latter  origi- 
nally existed.  Headache  is  very  frequent  and  is  caused  most  likely 
by  nerve  exhaustion.  It  is  most  often  frontal,  extending  to  the  tem- 
ples and  in  some  cases  to  the  occiput  and  nape  of  the  neck.  Ver- 
tical headaches  are  among  the  rarer  manifestations  of  refraction 
errors.      Perhaps    eye-strain    may  express  itself  in  the  form  of  a 

hemicrania. 
15 


2  26  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

The  pain  in  the  head  is  frequently  found  dependent  upon  the  use 
of  the  eyes,  but  may  be  constant,  ofttimes  comes  on  arising  in  the 
morning,  and  may  wear  away  as  the  day  progresses,  but  in  many 
the  pain  appears  only  towards  evening.  Nausea,  vomiting,  palpita- 
tion of  the  heart,  despondency,  neurasthenia  and  hysteria  are  fre- 
quently caused  by  eye-strain  as  well  as  twitchings  of  the  face-  or 
eye-muscles.  Astigmatic  errors  especially  and  the  kind  with  oblique 
axes  frequently  give  rise  to  tinnitus  aurium  and  vertigo,  simulating 
very  closely  an  incipient  internal  ear  trouble.  The  connections  be- 
tween the  eye  and  the  ear  will  be  pointed  out  in  a  subsequent  chapter. 
Hypennetropia,  also  hyperopia,  hypermetropy  and  hyperpresby- 
opia  {inrep,  over;  fierpov,  measure;  anjj,  eye),  denoted  by  H.,  is  an 
error  of  refraction  caused  by  the  retina  being  situated  anterior  to  the 
principal  focal  point  of  the  dioptric  system  of  the  eyeball.  As  par- 
allel rays  of  light  are  not  yet  come  to  a  focus  when  the  retina  of  the 
eye  intercepts  them  there  is  formed  upon  the  latter  an  area  of  illumi- 
nation the  shape  of  the  pupil,  and  varying  in  size  according  to  the 
amount  of  ametropia.  This  area  of  illumination  being  circular  in 
most  instances  is  spoken  of  as  a  circle  of  diffusion.  For  every 
point  in  the  object  there  is  formed  a  circle  of  diffusion,  and  by  the 
overlapping  of  these  circles  a  blurred  image  of  the  object  is  built  up. 
The  unaided  hyperopic  eye  has  no  point  of  clear  vision.  When  at 
rest  it  is  adjusted  for  converging  rays  of  light.  Such  do  not  natu- 
rally exist,  but  the  accommodation  can  render  parallel  rays  from  a 
distance  so,  and  bring  the  focus  of  them  upon  the  retina,  and  thus 

the  eye  is  given  sharp  distant  vision. 
A  convex  spherical  spectacle  lens 
does  the  same  thing  as  increased 
convexity  of  the  crystalline  lens  of 
the  eyeball  and  therefore  corrects 
the  hyperopia. 

Point  /'is  the  principal  focus  of  the  parallel  rays  A  and  A';  r,  the 
retina  lying  anterior  to  the  principal  focal  point  of  the  dioptric  system. 
In  figure  i  the  accommodation  is  represented  as  shortening  focal  in- 


NORMAL  AND  ABNORMAL  REFRACTION.  227 

terval  and  bringing  /'up  to  P' .  In  figure  2,  convex  spherical  lens  L 
takes  the  place  of  the  accommodation.  The  rays  A  and  A'  are  ren- 
dered convergent  by  it,  and 
then  by  the  aid  of  the  dioptric 
media  of  the  eyeball  are  brought 
to  a  focus  upon  the  retina  at  the 
point  P' .  If  one  diopter  of  ac- 
commodation or  a  one-diopter 
convex  spherical  lens  is  needed  to  bring  parallel  rays  of  light  to  a 
focus  upon  the  retina  of  an  eye  we  may  say  there  exists  one  diopter 
of  hyperopia.  One  diopter  of  H.  is  equivalent  to  an  actual  shorten- 
ing of  the  eyeball  of  .32  mm.  Beginners  are  often  confused  to  see 
how  a  lens  with  a  focal  length  of  one  meter  that  is  a  i-D.  lens  can 
correct  an  error  that  depends  upon  a  shortening  of  the  eyeball  of  only 
,32  mm.,  the  distance  between  the  retina  and  the  principal  focus  of  the 
dioptric  system  of  the  eyeball.  The  actual  antero-posterior  diameter 
of  the  emmetropic  eyeball  equals  24.2  mm.,  which  represents  a  refrac- 
tion of  41.3  D.  (1,000-^-24.2  =  41.3),  supposing  that  the  dioptric  sys- 
tem of  the  eyeball  to  be  replaced  by  a  single  refracting  surface,  in 
the  position  of  the  cornea  and  the  globe  filled  with  air.  A  shortening 
of  .32  mm.  of  the  eyeball  makes  its  diameter  23.88  mm.  (24.2  —.32  mm. 
=  23.88)  which  represents  the  focal  length  of  a  42  +  D.  lens,  one  diop- 
ter more  than  the  natural  strength  of  the  dioptric  media  of  the  eyeball 
to  be  supplied  by  a  convex  sphencal  lens  (100  cm.  h-  2.38  =  42  +  D.). 
If  a  2-D.  lens  is  needed  to  brmg  the  focus  of  parallel  rays  upon 
the  retina  the  error  is  equal  to  2  D.,  and  so  on.  For  any  given  dis- 
tance the  hyperope  has  to  accommodate  more  than  the  emmetrope, 
that  is,  the  same  amount  as  the  emmetrope  plus  the  amount  of  the 
hyperopia.  This  causes  the  hyperopic  eye  to  suffer  earlier  than  the 
emmetropic  eye  from  the  loss  of  accommodation  due  to  increasing 
age  of  the  patient.  The  hyperopic  eye  for  the  same  reason  fatigues 
sooner  than  the  emmetropic  eye,  other  things  being  equal.  It  is  de- 
prived of  the  periods  of  rest  that  the  emmetropic  eye  enjoys,  that  is, 
when  adjusted  for  a  distance.     We  have  H.  then  causing  eye-strain 


228  THE   E\E,    lis   REFRACTION   AND   DISEASES. 

or  blurred  vision  or  both,  H.,  in  the  largest  number  of  cases,  is  due 
to  an  antcro-posterior  shortening  of  the  eyeball,  axial  hyperopia. 
This  is  most  often  caused  by  a  diminution  of  the  eyeball  in  all  its 
diameters  and  not  alone  by  a  flattening  from  before  backwards. 
Other  less  frequent  causes  of  hyperopia  are  flattening  of  the  curves 
of  the  cornea  or  of  the  lens,  called  curvature  hyperopia,  and  a  low- 
index  of  refraction  of  the  crystalline  lens,  or  its  removal  from  the  eye- 
ball, index  hyperopia.  To  the  latter  class  belongs  the  H.  produced 
by  cataract  operations,  which  is  spoken  of  as  aphakial  hyperopia  (H. 
from  absence  of  the  lens). 

The  portion  of  the  figure  in  each  case  above  the  horizontal  line 
AB  represents  the  emmetropic  eyeball  in  section,  while  that  below 
the  error  of  refraction  produced  by  the  several  causes  respectively. 


Aphakial  H 


In  figure  i  the  hyperopic  eye's  retina  intercepts  the  light  at  P' 
before  it  comes  to  a  focus  ;  in  figure  2  the  lens  is  omitted  for  sake 
of  simplicity;  the  cornea  being  too  flat,  the  focal  point  is  thrown 
back  to  point  H,  which  lies  behind  the  retina  ;  in  figure  3  the  index 
of  the  lens  is  too  little  and  the  light  is  not  bent  enough  in  passing 
through  the  lens  to  be  focused  upon  the  retina,  but  would  come  to  a 
focus  at  the  point  H  if  the  retina  was  not  interposed ;  in  the  last 
figure,  the  light  as  it  enters  the  eyeball  is  only  refracted  by  the 
cornea,  aqueous  and  vitreous,  and  is  therefore  not  brought  soon 
enough  to  a  focus,  so  the  retina  receives  a  diffusion  circle  mstead  of 
a  focus.  Hyperopia  is  a  congenital  defect  and  is  never  acquired 
save  by  the  loss  of  the  crystalline  lens.  It  is  present  in  nearly  all 
eyes  to  a  certain  extent  at  birth.  Most  observers  believe  that  the 
amount  of  hyperopia  is  overcome  in  a  great  measure  as  the  child  gro'vs. 


NORMAL   AND   ABNORMAL   REFRACTION.  229 

Dr.  Randall  says  that  the  eyeball  increases  its  length  as  the  child 
grows,  from  about  16  mm.,  and  decreases  its  refraction  pari  passu,  so 
that  not  more  than  a  diopter  of  hyperopia  is  outgrown.  As  the  lens 
grows  it  increases  in  width,  faster  than  in  thickness,  which  causes  its 
curves  to  flatten  with  a  consequent  diminution  of  its  refraction. 

There  are  several  varieties  of  hyperopia  recognized  in  practice, 
based  upon  the  amount  of  accommodation  that  is  used.  The  amount 
of  error  that  remains  after  the  accommodation  is  exerted  to  its 
utmost  is  called  the  absolute ;  it  is  the  amount  of  hyperopia  that  the 
accommodation  can  not  cover  up  or  overcome. 

A  certain  amount  of  hyperopia  is  covered  by  the  action  of  the 
ciliary  muscle  and  revealed  by  the  relaxation  of  accommodation 
when  a  plus  spherical  lens  is  placed  before  the  eye.  This  amount 
of  hyperopia  that  can  be  covered  up  or  not  by  will  is  spoken  of  as 
the  facultative  hyperopia.  There  is  still  a  certain  amount  of  error 
that  remains  covered  after  the  strongest  convex  spherical  lens  is 
placed  before  the  eye  with  which  the  patient  maintains  the  same  dis- 
tant vision  as  without  and  which  remains  hidden  by  the  action  of 
the  ciliary  muscle.  From  early  childhood  the  ciliary  muscle  has  been 
active  and  the  habit  can  not  at  once  be  entirely  given  up.  This  por- 
tion habitually  covered  by  the  accommodation  is  called  the  latent 
hyperopia.  The  latent  hyperopia  is  never  entirely  revealed  in  folks 
under  60  years  of  age  unless  a  cycloplegic  be  instilled  into  the  eyes,  to 
paralyze  the  ciliary  muscles.  The  absolute  and  facultative  make  up 
the  manifest  hyperopia  or  the  amount  of  error  that  can  be  ascer- 
tained without  the  use  of  drugs  to  abrogate  the  function  of  the 
ciliary  muscle.  The  manifest  and  the  latent  together  make  up  the 
total  hyperopia.     The  scheme  on  following  page  illustrates. 

The  more  active  the  accommodation  is,  and  the  lower  the  degree 
of  hyperopia,  the  less  the  amount  of  absolute  hyperopia.  In  the 
young  the  amount  of  absolute  is  less  than  in  the  old,  as  in  the  latter 
the  accommodation  is  enfeebled.  More  and  more  of  the  latent 
becomes  manifest,  and  manifest  absolute  as  accommodation  fails 
incident  to  increasing  years. 


230 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


Hyperopia 


Absolute,  the  amount  exceeding  the  power  of 

accommodation. 
Facultative,  amount  corrected  or  not  accord 

ing  to  conditions. 
Voluntary. 


Manifest 
and 


Latent,  amount  habitually  covered  by  accom-  "I     Latent  equals 

"^o^^^^o"-  total  hyperopia. 

Involuntary.  J 


The  proportion  between  the  amount  of  latent  and  manifest  hyper- 
opia is  not  a  fixed  one,,  but  varies  in  different  individuals,  and  from 
day  to  day  or  from  minute  to  minute  in  the  same  eyeball.  The 
higher  degrees  of  hyperopia  alone  give  rise  to  trouble  in  childhood 
as  the  lower  amounts  can  be  overcome  by  the  act  of  accommoda- 
tion. The  earliest  symptom  arising  in  many  cases  in  children  is 
cross-eyes.  One  eye,  usually  the  one  that  has  the  higher  error  and 
the  poorer  vision,  turns  in  towards  the  nose  (internal  squint).  As 
the  accommodative  effort  in  hyperopia  is  necessarily  great  to  keep 
objects  well  in  focus,  some  of  the  nerve  influence  that  is  sent  to  the 
ciliary  muscle  overflows,  so  to  speak,  and  causes  contraction  of 
those  muscles  that  are  closely  associated  with  the  ciliary  muscle,  the 
internal  recti.  The  squint  may  only  be  apparent  when  there  is  most 
strain  upon  the  accommodation,  as  when  using  the  eyes  for  near 
work.  It  may  be  present  at  all  times  or  only  upon  occasions.  In- 
ternal squint  due  to  hyperopia  is  most  apt  to  occur  before  the  sixth 
year.  It  is  associated  with  high  but  not  with  the  highest  degrees  of 
refraction  error.  It  occurs  when  the  hyperopia  can  be  corrected  by 
straining  the  accommodation.  In  the  very  high  degrees  of  hyper- 
opia the  vision  is  found  below  par  when  the  error  is  properly  cor- 
rected by  convex  spherical  lenses,  caused  by  a  faulty  development  of 
the  eyeball  and  especially  of  the  retina.  The  deficient  vision  which  can 
not  be  made  perfect  by  accommodation  or  glasses  causes  the  child 
to  hold  his  reading  matter  very  close  to  the  eyes,  so  that  enlarged 
retinal  images  will  compensate  for  diminution  in  distinctness. 


NORMAL  AND  ABNORMAL  REFRACTION.  23 1 

Treatmerit.  —  No  drugs  or  means  of  any  sort  will  cause  the  eye- 
ball to  increase  its  antero-posterior  diameter  and  to  become  emme- 
tropic, or  to  do  away  with  any  of  the  causes  that  make  hyperopia. 
The  wearing  of  convex  spherical  lenses  in  spectacle  or  nose-glass 
frames  is  the  only  way  to  put  the  hyperopic  eyeball  in  the  same  posi- 
tion for  working  as  the  emmetropic  eye.  The  eye  is  said  to  have 
been  rendered  emmetropic  when  its  correcting  lens  is  adjusted.  The 
wearing  of  glasses  is  not  indicated  because  there  is  merely  hyperopia 
present,  but  from  the  evidences  of  eye-strain  alone.  The  rule  is  to 
correct  the  total  hyperopia,  unless  there  is  a  weakness  of  conver- 
gence, in  which  case  a  full  correction  of  the  hyperopia  would  exag- 
gerate the  muscular  anomaly  by  taking  off  the  extra  nerve  influence 
that  enables  the  interni  to  do  their  work,  received  through  the  effort 
on  the  part  of  the  accommodation  to  overcome  the  hyperopia 

Glasses  should  be  worn  only  for  near  work  if  the  eyes  do  not 
trouble  one  at  other  times,  if  they  annoy  whether  occupied  with 
near-seeing  or  not,  the  glasses  are  to  be  worn  all  the  time.  Many 
hyperopes  learn  how  to  look  at  distant  objects  with  relaxed  accom- 
modation and  are  therefore  comfortable  without  their  glasses.  The 
manner  of  determining  the  proper  glasses  for  hyperopia  will  be 
described  later. 

Myopia  (from  /xvetv,  to  close,  and  an/»,  eye,  so  called  from  the  man- 
ner myopes  have  of  partially  closing  the  eyes  to  increase  their  vision). 
—  Also  called  brachymetropia,  short-sightedness  or  near-sightedness. 
It  is  denoted  by  M. 

Myopia  is  the  error  of  refraction  that  results  from  the  retina  lying 
behind  the  principal  focus  of  the  dioptric  system  of  the  eyeball. 
Such  an  eyeball  can  not  by  any  means  bring  parallel  rays  of  light 
from  a  distance  to  a  distinct  focus  upon  its  retina.  It  is  adjusted  for 
divergent  rays  of  light  that  emanate  from  a  point  at  a  comparatively 
short  distance.  As  parallel  rays  of  light  come  to  a  focus  anterior  to 
the  retina  there  is  formed  a  diffusion  circle  upon  the  latter  by  the 
crossing  of  the  rays  of  light.  Parallel  rays  of  light  are  brought  to 
a  focus  upon  the  retina  by  passing  them  through  a  concave  spherical 


232  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

lens  placed  before  the  eye.  The  concave  lens  gives  to  the  light  the 
proper  divergence,  as  if  they  emanated  from  a  near  point,  for  which 
the  eyeball  is  adjusted  in  a  state  of  rest.  Concave  spherical  lenses 
then  correct  myopia.     In  the  figure  M  represents  a  myopic  eyeball 

bringing  rays  a  and  a'  to  a 

7  ^  ^V/'^  \      focus  in  front  of  the  retina. 

1^/"""--^^^:^::::;^---^^     The  concave  lens  L  inter- 

"°^~~~~  "■  \^---''lS^^^^^^-^^'''^^^^'\     posed  diverges  the  rays  to 

r^o'^^sC^^  /      b,  b',  and  thus  throws  the 

_l  \. — i;^ — ^         focus  back  upon  the  retina. 

(Divergent  rays  of  light  are  focused  posterior  to  parallel  rays.) 

The  rays  a  and  a'  have  the  same  divergence  after  passing  through 
lens  as  if  they  emanated  from  the  point  C. 

An  abnormally  long  antero-posterior  axis  of  the  eyeball  or  too 
great  a  curvature  of  its  refracting  media  may  be  inherited.  But  the 
great  mass  of  myopic  eyes  are  pathological  and  acquired.  They  are 
prone  to  take  on  distinct  and  characteristic  lesions,  that  may  be  due 
to  the  myopia,  but  which  on  the  other  hand  cause  an  increase  in  the 
latter.  The  sclera  of  the  eyeball  is  distended  normally  by  an  intra- 
ocular pressure  equal  to  25—30  mm.  of  mercury.  This  outward  push 
preserves  the  shape  of  the  eyeball.  The  normal  eye  dges  not  yield 
before  this  pressure  by  the  bulging  of  its  walls.  An  inherited  weak- 
ness of  the  eye-coats,  an  acute  disease,  or  a  diathesis  lowers  the 
resistance  of  the  sclera  to  withstand  this  intra-ocular  pressure. 
Furthermore  there  is  started  by  eye-strain  or  by  nutritive  deficiency, 
an  inflammatory  action  in  the  ocular  tunics  which  softens  them  and 
causes  them  to  bulge.  This  distention  mostly  always  occurs  at  the 
posterior  pole  of  the  eye-globe,  causing  myopia  or  the  increase  of  it, 
if  it  was  already  present,  by  the  elongation  of  the  antero-posterior 
axis. 

After  such  distention  begins  anything  that  favors  the  rise  of  intra- 
ocular tension  or  lowers  the  nutrition,  tends  to  cause  an  increase  in 
the  trouble.  The  most  important  factors  in  the  increase  of  myopia 
are  faulty  methods  of  using  the  eyes  during  school  life.     The  myopic 


NORMAL  AND  ABNORMAL  REFRACTION. 


233 


eyeball  is  a  long  one  and  does  not  readily  turn  in  the  orbit.  An 
excessive  effort  at  convergence,  due  to  holding  the  work  too  close  to 
the  eyes,  causes  pressure  upon  the  eyeballs.  It  is  squeezed  as  it 
were  between  the  internal  and  external  recti  muscles.  The  interni 
contract  to  maintain  single  binocular  fixation  at  the  reading  distance, 
and  the  externi  are  wrapped  tightly  around  the  globe.  To  maintain 
the  proper  amount  of  convergence  is  quite  a  task  for  the  myopes  of 
higher  degrees,  as  the  reading  matter  or  work  must  be  held  very 
close  to  the  eyes  in  order  that  there  may  be  received  distinct  retinal 
pictures.  Studying  in  a  stooped  posture,  causing  a  congestion  of 
the  neck,  head  and  eyeballs  is  deleterious. 

Bad  hygienic  surroundings  and  insufficient  light  are  to  be  blamed 
for  a  great  deal  of  increase  in  myopia  during  early  life.  Most  all 
cases  of  myopia  progress  to  a  certain  extent.  They  may  finally 
become  stationary  due  to  an  increase  in  the  resisting  power  of  the 
eye-tunics.  There  are  some  cases  of  myopia  that  continue  to  pro- 
gress, until  convergence  is  made  too  difficult  to  be  sustained,  when 
the  more  defective  eye  is  allowed  to  deviate.  Often  there  is  simply 
a  loss  of  binocular  fixation  for  near  objects.  The  power  of  conver- 
gence soon  diminishes  ;  the  internal  recti  become  weaker  from  non- 
use  and  finally  the  eyeball  is  turned  or  pulled  towards  the  temple  by 
the  stronger  external  rectus.  This  external  or  divergent  squint  may 
be  intermittent,  or  remittent  at  first.  After  the  squint  becomes  per- 
manent there  is  no  more  desire  on  the  part  of  the  eyes  to  converge 
and  consequently  the  myopia  is  most  apt  to  become  stationary.  In 
a  few  cases,  however,  the  sclera  has  become  so  thin  by  this  time  that 
it  continues  to  yield  before  the  intra-ocular  tension  and  eventually 
blindness  results.  To  these  cases  the  term  of  malignant  myopia  is 
given. 

After  the  sclera  has  become  attenuated  the  intra-ocular  pressure, 
and  the  tension  of  the  ocular  muscles  upon  the  eyeball  during  sleep 
undoubtedly  aid  in  the  increase  of  the  myopia.  The  eyeballs  are 
rolled  up  and  out  during  sleep  —  causing  the  globe  to  be  more  or 
less  squeezed   upon   by  the  superior  and   inferior   muscles.     The 


234  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

transverse  diameter  of  the  globe  is  thus  increased,  which  causes  the 
chorioid  to  be  dragged  upon  and  to  develop  inflammation  adjacent 
to  the  side  of  the  optic  nerve.  Sleeping  in  a  light  room  would 
further  increase  the  trouble,  inasmuch  as  the  eyes  would  be  rolled  up 
to  a  greater  extent  in  their  endeavor  to  rid  themselves  of  the  light. 

Myopia  reaches  a  much  higher  degree  than  hyperopia,  and  high 
myopia  constitutes  a  large  number  of  all  cases  of  myopia.  Myopia  of 
20  D.  is  as  common  as  hyperopia  of  half  that  amount.  Myopia  is 
designated  as  low  when  it  is  less  than  2.50  D.,  in  which  case  some 
accommodation  is  used  for  near  work.  Moderate  myopia,  from  2.50 
to  5  D.,  in  which  near  work  can  be  done  without  accommodation  ;  and 
high  myopia,  from  5  to  10  D.,  in  which  near  work  is  performed  at 
the  far-point.  Very  high  myopia  is  that  of  10  to  20  D.  or  more,  and 
is  usually  associated  with  extensive  inflammatory  changes  in  the  eye 
tunics.  It  is  often  detected  by  the  child  being  unable  to  see  the 
board  in  school  unless  he  takes  a  front  seat.  If  the  myopia  does  not 
exceed  3  D,  the  child  may  not  hold  the  reading  matter  closer  to  the 
eyes  than  is  proper ;  when,  however,  the  error  is  over  3  D.,  the  book 
must  be  held  closer  than  ^;^  cm.,  the  proper  reading  distance.  The 
patient  may  notice  spots  in  his  field  of  vision  due  to  opacities  in  the 
vitreous  humor.  The  pupil  of  the  myopic  eye  is  rather  larger  than 
in  the  emmetropic  because  less  often  exercised  by  contraction  in  the 
act  of  accommodation  and  convergence. 

Myopes  often  have  a  rather  vacant  and  stupid  stare  as  not  seeing 
well,  they  are  unable  to  respond  to  the  change  of  expression  of  the 
countenances  of  others.  They  show  a  distinct  inclination  for  read- 
ing and  pursuits  that  do  not  require  good  distant  vision.  With  the 
ophthalmoscope  there  are  seen  many  intra-ocular  changes  that  are 
indicative  of  the  cause  and  of  the  increase  of  the  myopia.  The  most 
frequent  are  alterations  in  the  chorioid  coat.  The  change  may  con- 
sist simply  in  congestion  or  edema,  causing  reddening,  blurring  of 
details  in  spots,  and  lighter  areas.  This  condition  is  spoken  of  as  a 
woolly,  patchy  or  fluffy  chorioid.  The  pigment  in  parts  of  the  fundus 
may  be  reduced,  while  in  other  parts  it  may  be  heaped  up  —  moth- 


NORMAL  AND  ABNORMAL  REFRACTION.  235 

eaten  fundus.     There  are  frequently  present  patches  of  chorioidal 
atrophy  or  active  inflammation  in  the  latter. 

The  characteristic  change  in  the  fundus  of  the  myopic  eyeball, 
however,  is  the  myopic  crescent.  This  consists  of  a  crescentic- 
shaped  area  of  chorioidal  atrophy  adjacent  to  and  upon  the  temporal 
side  of  the  optic  papilla.  The  crescent  arises  from  the  stretching  of 
the  eyeball  about  its  posterior  pole.  By  the  yielding  of  the  sclera, 
the  delicate  chorioid  coat  is  pulled  upon  and  readily  takes  on  an  in- 
flammatory action,  which  in  turn  gives  rise  to  atrophy.  There  may 
be  several  crescents  present,  the  one  to  the  outside  of  the  other. 
The  one  adjacent  to  the  nerve  will  consist  of  a  spot  of  complete 
atrophy,  the  next  one  of  partial  atrophy  and  the  most  external,  a 
spot  of  active  chorioiditis.  If  the  edge  of  the  crescent  is  well  and 
sharply  defined,  the  myopia  at  that  time  is  at  a  standstill ;  if  the  edge 
is  blurred,  on  the  other  hand,  active  inflammation  is  going  on,  indica- 
tive of  an  increase  in  the  elongation  of  the  eye-globe.  Sometimes  the 
crescent  is  of  a  more  or  less  triangular  form  and  then  it  is  called  a 
conus.  Both  the  crescent  and  the  conus  are  called  posterior  staphy- 
lomata,  or  the  crescent  or  conus  of  Scarpa.  The  optic  papilla  is 
tilted  by  the  recedence  of  the  sclera  and  is  therefore  seen  obliquely, 
causing  an  apparent  diminution  in  its  width,  appearing  as  a  narrow 
oval.  Late  in  the  course  of  high  myopia,  cataracts  and  vitreous 
opacities  develop  and  not  infrequently  detachment  of  the  retina 
follows. 

We  recognize  the  following  varieties  of  myopia:  Axial  myopia, 
so-called  because  the  antero-posterior  axis  is  too  long  as  compared 
with  the  focal  length  of  the  dioptric  system  of  the  eyeball.  It  is 
seldom  congenital ;  begins  as  eye-strain  ;  increases,  or  if  it  becomes 
stationary  in  early  life,  it  may  be  outgrown  by  the  slow  growth  of 
and  consequent  flattening  of  the  crystalline  lens.  Axial  myopia  may 
begin  in  middle  or  in  old  age  as  a  symptom  of  diabetes.  Curvature 
myopia  may  begin  at  any  time  ;  the  cornea  becomes  distended  in  a 
form  of  a  cone  or  globe,  due  to  weakness  of  its  fibers  brought  about 
by  poor  nutrition.     This  is  myopia  from  conical  cornea.     Index  my- 


236 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


opia  comes  in  old  age  as  a  precursor  of  cataract,  due  to  swelling  of 
the  crystalline  lens,  also  called  second  sight,  be- 
cause when  it  sets  in  the  patient  no  longer  needs 
his  convex  lenses  for  reading  and  for  seeing  near 
by,  but  is  able  to  throw  them  aside.  It  is  usually 
complicated  with  astigmatism  against  the  rule. 
Lastly,  spasmodic  myopia,  caused  by  a  spasmodic 
contraction  of  the  ciliary  muscle.  The  lens  is 
rendered  abnormally  convex  and  then  the  light 
from  a  distance  is  brought  to  a  focus  anterior  to 
the  retina.  This  spasm  is  most  apt  to  occur  in 
convergent  or  accommodative  inefficiency,  and  in 
low  degrees  of  hyperopia,  although  it  occurs  in 
emmetropia,  and  less  frequently  in  myopia,  in- 
creasing the  latter  error.  It  is  occasionally  uni- 
lateral, and  then  affects  the  eye  that  is  used  the 
most.  Spasm  of  accommodation  often  renders 
latent  a  considerable  amount  of  hyperopia.  In 
the  opposite  figures,  the  portions  above  the  hori- 
zontal line  represent  sections  of  emmetropia,  while 
those  below  the  line  represent  the  respective 
errors. 

Treatment.  —  Distant  vision  is  rendered  distinct 
by  the  use  of  concave  spherical  lenses,  and  if  the 
error  is  of  considerable  amount,  above  3  D.,  one 
is  enabled  by  the  use  of  concave  lenses  to  remove 
printed  matter  to  the  proper  reading  distance. 
The  progress  of  myopia  will  be  checked  perma- 
nently if  near  work  is  avoided.  If  on  the  increase 
in  a  school  child,  the  child  should  be  kept  from 
school  until  all  inflammatory  reaction  in  the  eye- 
ball has  subsided  and  then  the  most  careful 
hygiene  of  the  eyes  preserved.     Correcting  lenses 

in  the  vast  majority  of  cases  render  myopia  stationary.     Accommo- 


NORMAL  AND  ABNORMAL  REFRACTION.  237 

dation  and  convergence  are  both  accused  of  being  the  cause  of  the 
increase  in  myopia.  Accommodation  is  far  more  strained  in  hyperopic 
eyes,  but  such  eyes  seldom  show  any  tendency  to  elongate.  On  the 
other  hand  hyperopia  is  an  obstacle  to  the  straining  of  convergence 
while  myopia  favors  it,  as  the  accommodation  near  point  in  myopia 
lies  very  close  to  the  eyes.  Again  the  myopia  does  not  cease  to 
progress  when  the  accommodation  is  reduced  to  a  minimum,  or 
when  it  is  rendered  unnecessary  for  near  vision,  but  it  often  ceases 
when  convergence  is  not  needed,  as  when  single  binocular  fixation 
is  lost. 

Von  Graefe  was  the  first  to  advocate  the  undercorrection  of  myopia 
as  is  still  practiced  by  many.  He  noticed  with  the  ophthalmoscope 
that  there  developed  a  pulsation  of  the  retinal  veins  during  accom- 
modation and  therefore  said  if  accommodation  gave  rise  to  increased 
intra-ocular  tension  it  was  a  bad  thing  for  myopia.  Pulsation  of  the 
retinal  veins  occurs  however  in  many  eyes  under  the  full  effect  of 
atropine,  so  the  rise  of  tension  must  be  due  to  the  pressure  of  the 
extra-ocular  muscles  upon  the  eyeball.  That  this  is  the  correct  ex- 
planation is  proven  by  the  fact  that  no  pulsation  is  observable  during 
accommodation  in  cases  of  paralysis  of  the  extra-ocular  muscles. 

The  myope  should  then  have  glasses  that  prohibit  excessive  con- 
vergence. If  binocular  fixation  for  near  objects  is  lost  it  is  not  advis- 
able to  try  to  restore  it,  as  convergence  would  then  again  become 
active  in  increasing  the  error  of  refraction.  Myopes  should  wear 
their  glasses  constantly,  so  that  the  requirements  made  on  accom- 
modation will  act  as  a  check  upon  convergence.  As  vision  is  ren- 
dered more  distinct  at  the  proper  reading  distance  from  the  eyes,  by 
aid  of  the  glasses,  printed  matter  will  be  held  further  off,  and  thus 
convergence  relieved,  also,  the  myope  not  being  able  to  accommodate 
well  will  hold  his  reading  matter  as  far  from  the  eyes  as  is  consistent 
with  good  vision,  to  use  as  little  accommodation  as  possible.  Some 
advise  only  a  part  correction  of  the  error  with  the  idea  that  accom- 
modation may  react  injuriously  upon  the  eyes.  Too  weak  lenses 
however  often  prove  a  menace  to  the  welfare  of  the  eye.     Looking 


238  THE   EYE.    ITS    REFRACTION   AND    DISEASES. 

obliquely  through  their  edges  gives  better  distant  vision,  by  increas- 
ing their  spherical  effect.  The  patient  soon  discovers  this  fact,  and 
avails  himself  of  it. 

Looking  obliquely  through  a  lens  also  gives  it  the  effect  of  a 
cylinder,  which  subjects  the  eye  to  a  strain  similar  to  that  caused  by 
uncorrected  astigmatism  ;  a  strain  that  is  illy  borne,  as  it  is  constant 
in  its  operation.  Partial  correction  for  near  work  is  deleterious,  as 
then  objects  are  held  closer  than  is  safe.  In  myopia  give  the  full 
correcting  lenses  as  often  as  is  possible,  for  constant  use. 

Certain  exceptions  to  this  rule  exist.  If  presbyopia  has  set  in 
weaker  concave  lenses  must  be  given  for  near  work.  The  same  is 
the  case  if  there  is  weakness  of  accommodation  from  other  causes. 
Presbyopia  sets  in  late  in  cases  of  non-  or  under-corrected  myopias, 
as  there  is  no  need  of  the  usual  amount  of  accommodation,  and  its 
loss  is  therefore  not  noticed  until  far  advanced.  A  full  correction 
should  be  given  for  distance  and  a  lens  a  diopter  or  so  weaker  for 
near  seeing,  if  the  accommodation  is  below  par ;  until  the  ciliary 
muscle  becomes  stronger  from  proper  use.  The  myope  must  further 
learn  to  hold  all  near  work  as  far  from  the  eyes  as  possible.  Good 
light  and  good  large  print  should  be  demanded  always.  The  patient 
should  always  sit  with  his  or  her  back  to  the  light,  and  never  with  it 
shining  in  the  eyes  while  employed  at  near  work.  Prolonged  near 
work  is  to  be  avoided.  One  should  take  frequent  resting  spells,  to 
allow  relaxation  of  convergence.  Reading  in  a  stooped  or  recum- 
bent posture  should  not  be  allowed,  as  both  favor  ocular  congestion. 
If  there  is  any  chorioiditis  present,  atropine  should  be  instilled  and 
complete  rest  from  all  near  work  taken.  Correcting  lenses  should 
be  changed  as  the  myopia  increases  or  diminishes. 

Fukula  advised  the  removal  of  the  crystalline  lens  in  cases  of  very 
high  degrees  of  myopia.  Cases  of  18-20  D.  or  over  are  alone  suited 
for  operation  as  about  that  much  hyperopia  is  made  by  the  removal 
of  the  lens,  causing  more  nearly  emmetropia.  Of  course  the  eyeball 
is  then  devoid  of  accommodation,  but  in  no  worse  condition  than  an 
eye  that  has  been  operated  upon  for  cataract.     In  cases  where  cor- 


NORMAL   AND    ABNORMAL   REFRACTION. 


239 


recting  lenses  cannot  be  comfortably  worn  or  where  with  them  the 
patient  has  not  vision  good  enough  to  carry  on  his  avocation  in  life 
is  this  measure  alone  adopted.  Experience  has  shown  that  the 
operation  does  not  put  a  stop  to  the  increase  in  the  myopia,  as  was 
claimed  by  Fukula.  The  operation  is  not  contraindicated  by  the 
presence  of  inflammation  in  the  fundus  of  the  eyeball,  over  which  it 
exercises  no  influence,  for  good  or  bad.  The  operation  is  best  per- 
formed by  needling  the  lens,  and  in  people  over  thirty  years  of  age 
combined  with  a  subsequent  extraction  of  the  opaque  lens  substance. 
All  are  not  agreed  as  to  the  advisability  of  running  the  necessary 
risk  of  operation  and  of  a  subsequent  destructive  inflammation  for 
the  amount  of  benefit  derived  in  the  majority  of  cases. 

By  the  operation  the  visual  acuity  is  improved  by  the  increase  in 
size  of  retinal  images,  by  the  nodal  point  being  brought  up  to  the 
apex  of  the  cornea  and  inasmuch  as  the  concave  lenses  correcting 
the  error  likewise  considerably  diminished  the  size  of  the  retinal 
images. 

TABLE    OF    AXIAL    HYPEROPIA.       (lANDOLT.) 


Degree 

Amount 

Total  Length 

Degree 

Amount 

Total  Length 

of  Hyperopia. 

of  Shortening. 

of  Axis. 

of  Hyperopia. 

of  Shortening. 

of  Axis. 

0.0 

0.00  mm. 

22.824  mm. 

8.0 

2.28  mm. 

20.54  mm. 

05 

0.16 

22.67 

8.5 

2.41 

20.41 

I.O 

0.31 

22.51 

9.0 

2.53 

20.29 

»-5 

0.47 

22.35 

9-5 

2.66 

20.16 

2.0 

0.62 

22.20 

10. 0 

2.78 

20.04 

2-5 

0.77 

22.05 

10.S 

2.90 

19.92 

30 

0.92 

21.90 

II 

3.02 

19.80 

35 

1.06 

21.76 

12 

325 

19-57 

4.0 

1. 21 

21.61 

13 

3-49 

1935 

4-5 

1-35 

21.47 

14 

369 

19- 13 

50 

1.50 

21.32 

IS 

391 

18.91 

5-5 

1.62 

21.20 

16 

4.11 

18.71 

6.0 

1.76 

21.06 

17 

4-32 

18.50 

6.5 

1.90 

20.92 

18 

4.52 

18.30 

7.0 

2.03 

20.80 

19 

4.71 

18.11 

75 

2.16 

20.66 

20 

4.90 

17.92 

It  will  be  seen  from  the  table  that  the  shortening  in  axial  length  of 
the  eyeball  to  make  i  D.  of  error  is  .3  mm.  up  to  7  D.  beyond  which 
the  shortening  necessary  to  make  i  D.  of  hyperopia  is  less  thao 
.3  mm. 


240 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


TABLE    OF   AXIAL    MYOPIA. 


Degree 

Amount 

Total  Length 

Degree 

Amount 

Total  Length 

of  Myopia. 

of  Lengthening. 

of  Axis. 

of  Myopia. 

of  Lengthening. 

of  Axis 

0.0 

0.00  mm. 

22.824  nun. 

8.0 

2.93  mm. 

25.75  ™™. 

05 

0.16 

22.98 

8.5 

3-14 

25.96 

I.O 

0.32 

23.14 

9.0 

3-55 

26.17 

1-5 

0.49 

23-3' 

9-5 

3-58 

26.40 

2.0 

0.66 

23.48 

10. 0 

3.80 

26.62 

2-5 

0.83 

23-65 

10. 5 

403 

26.85 

30 

1. 01 

23-83 

II 

4.26 

27.08 

3-5 

1. 19 

24.01 

12 

4-73 

27.55 

4.0 

1-37 

24.19 

13 

5.23 

28.05 

4-5 

1-55 

24-37 

14 

5-74 

28.56 

5.0 

1.74 

24.56 

15 

6.28 

29.10 

5-5 

1-93 

24-75 

16 

6.83 

29.65 

6.0 

2.13 

24-95 

17 

7.41 

30.23 

6.5 

2.32 

25.14 

18 

8.03 

30.85 

7.0 

2.52 

25-34 

19 

8.65 

31.47 

7-5 

2.73 

25.55 

20 

931 

32.13 

Unlike  hyperopia  the  necessary  increase  in  the  axis  of  the  eyeball 
to  make  one  additional  diopter  becomes  larger  as  the  myopia  in- 
creases. A  certain  amount  of  shortening  of  the  eyeball  does  not  give 
rise  to  the  same  degree  of  hyperopia  as  the  same  extent  of  lengthen- 
ing of  the  eyeball  does  to  myopia,  on  account  of  the  relative  dis- 
tances of  the  principal  points  being  different  in  the  two  cases. 


CHAPTER   XVIII 

ABNORMAL    REFRACTICN  [continued).       ASTIGMATISM 

Astigmatism,  denoted  As.  (from  a,  not,  and  o-rty/aa,  a  point),  also 
called  astigmism,  is  the  error  of  refraction  due  to  an  inequality  of 
the  curvatures  of  the  dioptric  surfaces  of  the  eyeball,  in  different 
meridians.  The  error  is  so  named  because  the  refraction  being-  dif- 
ferent in  different  meridians  of  the  astigmatic  eye,  a  point  of  light  is 
not  focused  upon  the  retina  as  a  point  of  light,  but  as  a  line  or  in 
the  form  of  an  ellipse.  In  an  astigmatic  eyeball,  then,  the  form  of 
the  retinal  illumination  from  a  point  of  light  is,  according  to  the  posi- 
tion of  the  retina,  one  of  the  following  : 


o  0 


This  can  be  demonstrated  by  taking  a  sphero-cylindrical  combina- 
tion and  moving  it  backward  and  forward  before  a  screen  upon 
which  is  thrown  the  focus  of  a  luminous  point  or  small  luminous 
circle.  As  the  position  of  the  screen  is  altered,  the  area  of  illumi- 
nation upon  the  screen  will  be  seen  to  change  its  shape,  gradually 
passing  through  the  series  of  figures  as  shown  above.  If  the  cylin- 
drical lens  in  the  combination  is  tilted  so  that  its  axis  is  inclined  the 
lines  and  ellipses  will  likewise  be  inclined  either  in  the  same  direc- 
tion or  in  the  opposite  direction  according  to  the  position  of  the 
screen. 

The  astigmatic  defect  is  either  resident  in  the  cornea,  lens  or 
retina.  When  the  location  of  the  error  is  not  designated  it  is 
assumed  to  be  located  in  the  cornea,  but  in  the  vast  majority  of 
cases  it  resides  in  the  lens  as  well.  The  astigmatic  cornea  is  well 
illustrated  by  a  circular  section  taken  from  the  edge  of  a  watch, 
i6  241 


242  THE   EYE.    ITS    REFRACTION   AND    DISEASES. 

curved  in  one  direction  and  more  curved  in  the  direction  at  right 
angles  thereto.  Regular  astigmatism  is  a  curvature  ametropia  in 
which  the  different  meridians  are  equally  curved  throughout  their 
course,  and  in  which  the  meridians  of  the  greatest  and  the  least 
refraction  are  at  right  angles  to  each  other.  Irregular  astigmatism 
is  that  in  which  either  of  the  above  conditions  of  regular  astigmatism 
is  departed  from,  or  produced  by  an  oblique  position  of  the  screen, 
the  retina.  This  latter  occurs  in  cases  of  myopia,  where  the  macula 
is  not  at  the  summit  of  the  posterior  staphyloma,  but  upon  its  side, 
and  operates  to  render  the-  vision  imperfect  in  certain  cases  of 
myopia.  Irregular  astigmatism  is  also  produced  by  an  oblique  posi- 
tion of  the  crystalline  lens  of  the  eyeball,  known  as  astigmatism  by 
incidence. 

The  meridians  of  the  greatest  and  the  least  curvatures  in  astig- 
matism are  called  the  principal  or  chief  meridians.  If  they  are  verti- 
cal and  horizontal,  the  astigmatism  is  styled  as  vertical  or  horizontal, 
according  to  the  direction  that  the  meridian  of  the  greatest  ametropia 
takes.  If  the  principal  meridians  are  oblique  or  inclined  to  the  ver- 
tical and  horizontal,  the  astigmatism  is  classed  as  oblique.  The 
cornea  on  its  anterior  surface  is  normally  slightly  more  curved  from 
above  downward  than  from  side  to  side  (the  radii  of  curvature  dif- 
fering by  about .  i  mm.).  In  the  majority  of  cases  the  anterior  or  the 
posterior  surface  of  the  lens  or  both  compensate  for  this  inequality, 
by  having  their  weakest  curves  in  direction  at  right  angles  to  the 
strongest  curve  of  the  cornea,  and  vice  versa.  As  this  inequality  in 
the  corneal  meridians  is  a  rule  in  eyes,  an  exaggeration  of  it  gives 
rise  to  what  is  termed  astigmatism  with  the  rule  (direct  astigmatism); 
while  if  the  cornea  is  most  bulged  or  curved  from  side  to  side,  we 
have  astigmatism  against  the  rule  (indirect  astigmatism).  The  figure 
illustrates  the  manner  in  which  light  is  refracted  on  entering  an 
astigmatic  eyeball.  The  lens  of  the  eyeball  in  the  diagram  is 
omitted  for  the  sake  of  simplicity. 

Parallel  rays  of  light  A,  A'  from  a  distant  point  pass  into  the  eye- 
ball through  the  more  bulged  vertical  meridian  of  the  cornea,  which 


ABNORMAL   REFRACTION.  243 

with  the  aid  of  the  lens  and  the  vitreous  brings  them  to  a  focus  upon 
the  retina,  and  therefore  the  vertical  meridian  of  the  eye  is  called 
emmetropic.  Parallel  rays  B,  B'  from  the  same  point  pass  to  the 
eyeball  through  the  cross,  flatter  meridian  of  the  cornea.  The  re- 
fraction being  feebler  in  this  meridian  the  focus  lies  behind  the  retina 
at  the  point  H' .  The  cross  meridian  of  the  eyeball  is  therefore  called 
hyperopic.  If  one  of  the  principal  meridians  is  emmetropic,  the 
astigmatism  is  spoken  of  as  simple ;  if  both  principal  meridians  are 
hyperopic  but  the  one  more  so  than  the  other,  as  compound  hyper- 
opic ;  if  both  are  myopic,  but  to  different  degrees,  as  compound  my- 
opic.    While  if  one  principal  meridian  is  hyperopic',  and  the  other  one 


myopic,  the  astigmatism  is  called  mixed.  The  form  of  illumination 
at  the  point  E\  in  the  preceding  figure,  where  all  the  rays  from  a 
common  external  point  come  to  a  focus,  is  that  of  a  horizontal  line, 
while  that  at  the  point  H' ,  where  they  again  come  together,  is  a  ver- 
tical Hne.  These  lines  are  called  the  focal  lines  of  the  astigmatism. 
The  distance  between  the  first  and  the  second  focal  lines  is  the  in- 
terval of  Sturm.  The  length  of  this  interval  represents  the  amount 
of  astigmatism.     The  smaller  it  is  the  less  is  the  astigmatism,  and 


vice  versa. 


The  first  or  the  anterior  focal  line  is  formed  by  refraction  through 
the  greatest  refracting  meridian  of  the  eyeball  and  is  at  right  angles 
to  the  direction  of  the  latter.  The  second  focal  line  is  formed  by  the 
least  refracting  meridian  and  is  at  right  angles  to  that  meridian.     The 


244 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


diffusion  spots  are  everywhere  elliptical  except  at  one  point  between 
the  focal  lines,  where  the  spot  is  circular  in  outline.  The  rays  of 
light  that  pass  through  the  principal  meridians  meet  the  axis  at  their 
respective  focal  points,  but  the  light  that  passes  into  the  eye  through 
secondary  axes  does  not  meet  the  axis  of  the  dioptric  system  of  the 
eyeball.  The  following  method  of  calculating  the  length  of  the  focal 
lines  is  according  to  Tscherning.  The  length  of  these  lines  is  pro- 
portional to  their  distances  from  the  lens. 

In  the  figure  let  P  be  the  diameter  of  the  lens  ;  F',  the  first  focal 


P— Horizontal  Focal  Line,  P^*  Vertical  Focal  Line 


line  ;  F'\  the  second  focal  line  ;  P'  and  P^,  the  lengths  of  the  two  focal 
lines  respectively.     Then  in  the  two  triangles,  we  have 

P'IP=       ^f  ,  2indP^IP= 


F" 


F' 


by  dividing  P' [ P""^  F'lF". 

The  circle  of  diffusion  is  at  a,  where  the  diameters  are  equal.  It 
divides  the  interfocal  distance  into  two  parts  proportional  to  the  focal 
distances.  Designating  the  diameter  of  this  circle  by  a,  and  the  two 
parts  of  the  interfocal  distance  by  x  and  y  we  have  : 

aj P'  =ylx-{-y,  and  a/P^  =  x/x+y,  and  by  dividing 

ylx  =  PyP'  =  F"IF'. 

All  other  diffusion  spots  are  ellipses,  of  which  it  is  not  difficult  to 
calculate  the  axes.     If  the  screen  is  placed  at  the  distance  d,  from  the 


ABNORMAL   REFRACTION. 


245 


second  focal  line  we  see  that  the  axes  c  and  d  are  found  by  the  fol- 
lowing equations  : 

c^^b-{F"-F')       ,  d _  b 
p  pf  and  p-^,, 

equations  which  give  as  the  relation  between  the  axes : 

^^b-(F"-F')     F" 

d  T'        ^X- 

Knowing  the  axes  we  can  find  the  ellipse  by  construction.  W^ 
make  a  circle  with  half  the  length  of  d  (previous  figure)  for  its  radius, 
and  draw  within  two  diameters,  a  ver- 
tical one  and  a  horizontal  one.  The 
points  A'  and  E'  are  then  marked  so 
that  0A'  =  cl2.  BD  and  A'E'  are 
then  the  two  axes  of  the  ellipse. 

We  can  find  any  point  G\  of  the 
ellipse,  by  letting  fall  a  perpendicular 
GH  to  the  long  axis  so  that 

G'HlGH=c\d. 

This  same  construction  can  be  used 
to  find  the  course  of  rays  that  do  not 

lie  in  the  principal  planes.  If  the  dioptric  system  were  spherical 
and  of  the  power  of  the  meridian  of  the  least  refraction,  we  would 
get  a  circle  of  diffusion  of  the  diameter  BD.  This  circle  would  only 
be  a  diminished  image  of  the  lens  and  it  would  be  easy  to  determine 
the  position  of  the  point  K,  through  which  the  ray  would  pass.  We 
then  can  find  the  point  K'  by  diminishing  the  distance  of  K  from 
the  long  axis  in  the  proportion  of  cjd. 

Lines  that  run  in  different  directions  are  seen  unequally  distinct 
by  the  astigmatic  eye.  A  line  is  distinct  or  not  according  to  whether 
its  edges  are  well  focused  or  not.  The  distinctness  of  vertical  lines 
depends  upon  the  accuracy  of  focusing  through  the  horizontal  merid- 
ian of  the  eye,  and  so  with  any  line,  it  is  distinctly  seen  if  the  meridian 


^^^ 

a'- 

s 

Z*^   .-' 

-~-»^ 

>^ 

^^ 

d 

*'v       X 

N       X 

I  • 

.K 

^v\ 

f/ 

•K' 

*\\ 

0 

H                  1 

\\ 

\  \ 

•    / 

\     N. 

^ 

•^      / 

C^^^-~~ 

E_ 

^^   y 

^^ 

^ 

^ 

246 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


The  transposition  in  refraction  causing  a  point  above 
in  the  line  to  appear  below  in  its  image,  etc.,  has  been 
omitted  for  simplicity. 


of  the  eyeball  at  right  angles  to  its  direction  forms  a  clear  retinal 
picture  of  it. 

In  the  figure  let  a,  b  and  c  represent  three  horizontal  meridians  of 
the  cornea  C;  d,2i  vertical  meridian  of  same.  In  the  vertical  line  L 
there  are  three  points,  the  one  above  the  other,  and  what  is  true  of 

these  three  points  is  true  of  the 
whole  line,  as  the  line  is  built  up 
of  the  apposition  of  the  points 
that  compose  it. 

Point  I  sends  rays  of  light 
to  meridian  a,  and  is  focused  at 
the  point  i',  behind;  lights  from 
points  2  and  3  pass  through 
meridians  b  and  c  respectively 
and  are  focused  at  points  2'  and 
3',  The  image  of  the  line  L  is 
then  built  up  by  juxtaposition 
of  the  images  of  the  points  in  the  line  L.  5  and  6  are  two  rays  that 
enter  the  cornea  through  the  vertical  meridian  d,  which  is  more  curved 
than  the  horizontal  meridians  and  therefore  has  a  shorter  focal  length, 
and  brings  the  rays  to  a  focus  at  the  point  O,  before  the  screen  is 
reached.  The  rays  diverge  again  from  the  point  O  and  form  an  area 
of.illumination  upon  the  screen  the  shape  of  a  vertical  line.  By  the 
overlapping  of  the  short  lines,  the  line  L'  is  built  up.  It  is  evident, 
therefore,  that  as  long  as  the  cross  focusing  of  points  in  line  L  is 
accurate,  the  vertical  line  L'  is  distinct.  The  only  blurring  of  the 
line  will  be  at  its  ends,  where  the  rays  of  light  from  the  end  points 
of  L  pass  through  the  vertical  meridians  of  the  cornea.  An  ocular 
demonstration  of  this  fact  is  as  follows  :  Look  at  crossed  lines  through 
a  strong  convex  or  concave  cylindrical  lens,  say  one  of  2  D.,  so  as  to 
have  the  test  decisive  ;  and  it  will  be  seen  that  the  lines  at  right 
angles  to  the  direction  of  the  axis  of  the  cylinder  before  the  eye  are 
seen  the  better.  The  refraction  of  the  eyeball  is  not  changed  by 
the  cylinder  in  the  direction  of  its  axis,  and  therefore  the  cross  lines 


ABNORMAL   REFRACTION. 


247 


are  seen  well  as  the  focusing  of  them  through  the  vertical  meridian 
is  not  interfered  with  when  the  axis  of  the  cylinder  is  held  vertically. 
The  same  fact  is  well  proven  by  photography.  Focus  a  cai^era  for 
crossed  lines  and  then  place  a  cylin- 
drical lens  with  its  axis  vertical  across 
the  lens  of  the  instrument,  and  then 
take  the  picture  of  the  lines.  It  will 
be  seen  that  the  horizontal  lines  are 
distinctly  taken  while  the  vertical 
ones  are  very  indistinct, 

DIAGRAMS    ILLUSTRATING   THE    FOCUS- 
ING   IN    DIFFERENT   VARIETIES 
OF   ASTIGMATISM. 

V  focusing  through  the  vertical 
meridian  of  the  eye,  and  H  that 
through  the  horizontal  meridian. 
The  rays  are  represented  parallel 
as  they  enter  the  eye.  Each  one 
save  that  of  compound  myopic  astig- 
matism is  a  case  with  the  rule,  the 
vertical  meridian  of  the  cornea  be- 
ing more  bulged  than  the  horizontal 
one. 

Astigmatism  may  be  acquired  from 
the  habit  of  closing  one  eye  while 
looking  through  an  optical  instru- 
ment with  the  other  one.  The  pres- 
sure of  the  tightly  closed  lids  upon 
the  cornea  finally  leads  to  altera- 
tion in  its  nutrition  and  curves.  There  is  usually  remaining  a  high 
degree  of  astigmatism  against  the  rule  after  cataract  extraction 
operations,  caused  by  the  healing  of  the  transverse  wound  in  the 
cornea,  and  consequent  flattening  of  its  vertical  curve.     The  axis  as 


248  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

well  as  the  amount  of  astigmatism  may  undergo  a  change  in  the  course 
of  time,  and  especially  in  those  with  a  rheumatic  or  gouty  diathesis, 
as  pointed  out  by  Dr.  Lautenbach,  The  action  of  the  extra-ocular 
muscles,  too,  perhaps  has  an  effect  over  the  nature  and  amount  of 
the  corneal  astigmatism  (see  discussion  of  errors  of  refraction  caused 
by  the  extra-ocular  muscles,  at  end  of  chapter). 

By  the  elongation  of  the  eyeball  due  to  eye-strain,  a  hyperopic 
meridian  would  of  course  first  become  emmetropic  and  finally  myopic, 
transforming  the  case  of  simple  hyperopic  astigmatism  into  one  of 
simple  myopic  astigmatism. 

Symptoms  of  Astigmatism.  —  Lines  that  run  in  the  direction  of  one 
of  the  principal  meridians  of  the  eye  can  alone  be  seen  distinctly,  in 
the  majority  of  cases,  although  in  some,  by  an  effort  of  accommoda- 
tion, all  the  lines  in  the  radiating  star-figure  used  for  detecting  astig- 
matism may  be  made  to  appear  equal  in  distinctness.  There  exists 
a  very  characteristic  diminution  of  visual  acuity  in  astigmatism. 
Some  letters  are  more  blurred  than  others  of  the  same  size,  due  to 
the  direction  of  their  strokes.  Curved  letters  are  furthermore  not 
seen  as  distinctly  as  straight-line  ones.  The  indistinctness  of  print 
produced  by  astigmatism  is,  however,  not  more  than  half  as  great  as 
that  produced  by  hyperopia  or  myopia  of  equal  amDunt,  when  the 
eyes  are  not  using  their  accommodation.  Some  have  claimed  that 
the  astigmatic  eyeball  endeavors  to  correct  its  anomaly  by  unequal 
contraction  of  the  ciliary  muscle  in  different  meridians,  causing  the 
lens  to  become  more  convex  in  one  meridian  than  in  another,  or  pos- 
sibly by  the  tilting  of  the  crystalline  lens,  giving  rise  to  an  astigmatism 
of  incidence,  of  the  opposite  nature  to  the  inherent  error.  It  is  not 
demonstrable  that  either  of  these  phenomena  ever  occurs.  It  is  more 
likely  that  the  astigmatic  eye  covers  up  its  error  by  a  rapid  change  in 
the  accommodation,  so  as  to  bring  a  sharp  focus  of  the  object  through 
each  meridian,  upon  the  retina,  in  rapid  succession,  so  that  these  im- 
pressions may  add  in  a  single  mental  impression. 

The  theory  of  sectional  accommodation  was  first  advocated  by 
Martin,   for  the  relief  and  correction  of  astigmatism.     The  ciliary 


ABNORMAL   REFRACTION.  249 

muscle  according  to  this  theory  is  supposed  to  act  in  two  opposite 
sections,  while  the  balance  of  the  circular  muscle  remains  quiet  or 
only  in  slight  action.  The  parts  of  the  muscle  in  greatest  action  are 
supposed  to  coincide  with  the  corneal  meridian  of  least  curvature, 
the  lenticular  astigmatism  neutralizing  the  effect  of  the  corneal  error. 
If  this  is  true  the  ciliary  muscle  is  the  only  sphincter  muscle  in  the 
body  that  is  able  to  contract  in  sections.  It  is  most  likely  that  sec- 
tional accommodation  does  not  occur  as  the  ciliary  muscle  is  not 
innervated  in  sections  by  different  nerves,  but  the  same  nerve  from 
one  nucleus  or  center  presides  over  the  action  of  the  entire  muscle. 
If  sectional  accommodation  does  occur  it  is  of  no  avail  in  myopic 
astigmatism,  as  it  could  do  nothing  but  convert  the  case  into  one  of 
simple  myopia,  In  which  case  the  vision  would  be  rendered  poorer. 
Eye-strain  only  exists  when  by  it  the  vision  can  be  rendered  better, 
and  when  this  cannot  be  accomplished,  the  strain  is  not  instituted. 

This  effort  on  the  part  of  the  ciliary  muscle  leads  to  all  the  symp- 
toms of  eye-strain.  High  degrees  of  myopic  astigmatism  as  myopia 
causes  squinting  or  partial  closure  of  the  eyelids  to  increase  the 
visual  acuity.  This  as  in  myopia  may  give  rise  to  an  irritable  con- 
dition, with  secondary  disturbances  in  the  cornea.  We  not  infre- 
quently have  internal  strabismus  associated  with  hyperopic  astigma- 
tism, and  external  strabismus  with  myopic  astigmatism.  Oblique 
astigmatism  causes  a  strain  upon  the  oblique  muscles  of  the  eyeball, 
because  the  focal  lines  are  inclined  and  occupy  oblique  meridians 
upon  the  retina.  The  eyes  would  then  see  everything  slanting  in 
space  unless  there  was  a  rotation,  so  that  the  usually  vertical  meridians 
of  the  retinae  were  brought  to  coincide  with  the  meridians  of  stim- 
ulation, or  a  physiological  compensation  for  the  obliquity  of  the  retinal 
images.  In  cases  where  glasses  have  never  been  worn  undoubtedly 
the  oblique  meridians  of  the  retina  answer  for  objects  vertical  in  space, 
as  it  is  rare  that  such  a  case  sees  vertical  objects,  slanting  in  space,  but, 
when  the  correcting  cylinders  are  worn,  and  the  retinal  Images  are 
rendered  more  upright  thereby,  the  patients  will  often  complain  for  a 
varying  length  of  time  that  the  glasses  cause  a  slantine^  of  objects, 


250  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

which  will,  if  notice  be  taken,  be  found  to  occur  in  the  direction 
opposite  to  the  inclination  of  the  axis  of  the  correcting  cylinders, 
in  hyperopic  astigmatism  and  in  the  same  direction  in  myopic  astig- 
matism. (For  further  consideration  of  the  action  of  the  oblique 
muscles  in  oblique  astigmatism  see  chapter  upon  Muscular  Errors.) 

It  is  believed  by  some  that  the  tension  of  the  extra-ocular  muscles 
upon  the  eye-globe  impart  to  it  its  characteristic  refraction  and  is 
capable  of  causing  a  decided  change  in  its  refraction.  The  sclera 
being  more  or  less  yielding  and  surrounded  by  the  four  recti  muscles, 
its  shape  is  said  to  depend  somewhat  upon  the  tension  of  these 
muscles  upon  the  eye-globe.  It  is  claimed  that  undue  tension  of  all 
four  recti  muscles,  by  drawing  the  eye-globe  back  against  the  cushion 
of  fat  behind  it,  shortens  its  antero-posterior  diameter,  giving  rise  to 
hyperopia,  and  that  anomalous  tension  in  the  pair  of  vertically-acting 
muscles  aided  by  the  weight  of  or  sinking  down  of  the  vitreous 
humor  which  does  not  entirely  fill  the  globe,  gives  rise  to  change  of 
form  of  the  cornea  resulting  in  astigmatism  against  the  rule,  while  on 
the  other  hand  overaction  of  the  vertical-acting  muscles  causes  astig- 
matism with  the  rule,  and  anomalous  tension  of  the  oblique  muscles, 
oblique  astigmatism.  Shulin  says  that  instead  of  internal  squint 
being  caused  by  hyperopia  it  is  more  likely  that  the  hyperopia  is  caused 
to  increase  by  the  internal  squint.  The  above  is  entirely  hypothet- 
ical. If  it  were  true  we  should  find  a  decrease  in  the  amount  of 
ametropia,  after  the  instillation  of  atropia  which  causes  a  disappear- 
ance of  the  squint,  but  this  is  not  the  case,  or  again  there  is  observed 
no  alteration  in  the  refraction  of  the  eye  after  operations  upon  the 
eye  muscles.  The  tension  of  the  extra-ocular  muscles  may  play  some 
part  in  the  ocular  refraction,  especially  astigmatism,  but  so  far  no 
alteration  of  the  curves  of  the  cornea  has  been  noted  after  the  action 
of  the  muscles  has  been  abrogated  by  paralysis  or  operations.  The 
effect  of  muscular  tension  upon  the  production  and  increase  of  myopia 
has  already  been  pointed  out. 

Treatment  of  Astigmatism. — Astigmatism  is  corrected  by  the  use 
of  cylindrical  lenses,  convex  or  concave  as  the  case  may  be.     In 


ABNORMAL   REFRACTION.  25 / 

compound  astigmatism,  which  is  nothing  more  than  hyperopia  or 
myopia  with  astigmatism  added,  there  is  needed  a  spherical  lens  to 
correct  the  hyperopic  or  myopic  error  and  a  cylindrical  lens  combined 
with  it  for  the  astigmatism.  Such  a  combination  of  lenses  is  spoken 
of  as  a  sphero-cylindrical  combination.  The  lens  that  corrects  the 
astigmatic  error  causes  all  parallel  rays  that  enter  the  eye,  no  matter 
through  what  meridian,  to  be  focused  upon  the  retina. 

Any  astigmatic  case  may  be  corrected  by  one  of  three  combina- 
tions of  lenses.  Suppose  for  example  that  we  have  a  compound 
hyperopic  case  in  which  the  vertical  meridian  of  the  eye  is  hyperopic 
to  4  D.,  and  the  horizontal  meridian  hyperopic  to  i  D.  (astigmatism 
against  the  rule).  The  amount  of  astigm'atism  in  this  case  is 
4  —  I  =3  D.)  3  D.  This  amount  of  astigmatism  can  be  corrected  by 
a  +  3  D.  cylinder  with  its  axis  at  i8o°,  that  is  with  the  active  plane 
or  curved  side  of  the  cylinder  placed  vertically.  There  still  remains 
uncorrected  i  D,  of  hyperopia,  which  needs  the  addition  of  a  i  D.  S. 
The  first  method  then  is  the  following : 

+  1  D.  S.  +  3  D.  cylindrical  axis  i8o°. 

Secondly,  the  case  may  be  corrected  by  a  concave  cylinder  with  its 
acting  plane  crosswise  (axis  vertical),  lengthening  the  focal  interval 
in  that  meridian,  thus  causing  the  same  amount  of  error  in  both  the 
vertical  and  horizontal  meridians  of  the  eye.  There  would  then  be  left 
4  D.  of  hyperopia  to  be  corrected  by  the  addition  of  a  4  D.  S.  lens. 
Such  a  combination  would  be  written  thus  :  +  4  D.  S.  —  3  D.  cylin- 
drical axis  90°. 

Lastly,  the  ametropia  may  be  corrected  by  the  employment  of 
crossed  cylinders,  that  is  by  two  cylinders  with  their  axes  at  right 
angles  to  each  other.  Thus:  +4D.  cylindrical  axis  180°,  +  i  D. 
cylindrical  axis  90°. 

Of  these  three  combinations  it  will  be  seen  that  the  first  has  the 
least  or  the  weakest  curved  surfaces.  It  is  most  free  from  spherical 
aberration  and  the  lenses  can  be  ground  much  thinner.  Such  a 
combination  with  the  cylinder  and  the  sphere  of  like  signs,  either 


252  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

plus  or  minus,  is  the  combination  that  should  always  be  employed 
when  possible.  This  is  always  possible  save  in  cases  of  mixed 
astigmatism.  (Any  combination  in  which  the  cylinder  is  of  less 
strength  than  the  sphere  and  of  opposite  sign  can  be  reduced  to 
simpler  terms  or  like  signs.)  Crossed  cylinders  should  always  be 
avoided  as  they  cannot  be  ground  with  the  same  degree  of  accuracy 
as  their  equivalents.  Astigmatics  should  as  a  rule  wear  their 
glasses  all  the  time.  If  after  a  while  the  patient  learns  to  look  in 
the  distance  with  relaxed  accommodation,  as  the  emmetrope  does, 
he  may  do  without  them  for  distance,  if  so  doing  causes  him  no 
headache  or  eye-pain.  Myopic  astigmatism  as  a  rule  gives  rise  to  no 
strain  for  distant  seeing,  as  the  myopic  astigmatic  eye  can  not  aid 
itself  by  accommodation,  therefore  glasses  for  distance  may  be  'dis- 
pensed with  more  readily  than  in  cases  of  hyperopic  astigmatism. 

Irregular  Astigmatism. — Irregular  astigmatism  can  not  be  cor- 
rected by  the  use  of  lenses.  It  is  caused  by  corneal  disease  giving 
rise  to  a  distortion  of  the  corneal  surface,  either  through  ulceration 
or  by  an  alteration  of  its  curves,  as  in  conical  cornea,  or  the  closely 
allied  form  of  globular  cornea.  Cataract  by  altering  the  refraction 
of  the  lens  in  different  meridians,  and  in  different  parts  of  the  same 
meridian,  gives  rise  to  irregular  astigmatism.  Obliqyity  of  the  crys- 
talline is  another  cause,  whether  congenital  or  caused  by  a  partial 
dislocation  of  the  lens. 

Obliquity  of  the  crystalline  lens  causes  what  is  called  astigmatism 
by  incidence.  Place  a  spherical  lens  at  some  distance  from  a  lumi- 
nous point  and  catch  the  image  of  this  point  upon  a  screen.  If  the 
lens  is  rotated  around  a  vertical  axis,  the  screen  ceases  to  be  at  the 
point ;  it  must  be  moved  nearer  the  lens  and  at  the  same  time  it  is 
seen  that  the  pencil  is  astigmatic.  The  horizontal  focal  line  is  at  a 
greater  distance  from  the  lens  than  the  vertical  focal  line. 

The  refraction  has  increased  in  both  meridians,  but  more  in  that 
which  contains  the  axis  of  the  lens.  The  focal  lines  are  not  distinct, 
especially  if  a  small  diaphragm  is  not  used.  They  are  rather  dif- 
fusion spots  drawn  out  in  one  direction.     The  pencil  has  one  true 


ABNORMAL   REFRACTION.  ^53 

focal  line,  however,  which  is  horizontal,  if  the  lens  is  rotated 
around  a  vertical  axis.  We  can  find  it  by  rotating  the  screen 
around  a  vertical  axis,  but  in  a  direction  the  reverse  of  that  of  the 
lens. 

A  pencil  reflected  or  refracted  obliquely  by  a  spherical  surface  is 
also  astigmatic  by  incidence  ;  the  same  is  true  of  refraction  obliquely 
through  plane  surfaces.  All  mirrors  have  this  defect  due  to  the 
thickness  of  the  glass  in  front  of  the  coating. 


AS.  BY  INCIDENCE 


Let  abed  be  an  incident  beam  of  light  parallel  to  the  primary  axis 
of  a  refracting  spherical  surface.  Suppose  that  the  beam  is  cylin- 
drical, so  that  ab  is  the  diameter  of  a  small  round  portion,  represent- 
ing the  aperture  of  the  surface.  Ab  is  one  of  the  principal  meridians 
of  the  surface  and  the  meridian  at  right  angles  to  ab,  the  other.  On 
account  of  spherical  aberration,  the  ray  aF'  is  refracted  more  and 
reaches  the  axis  of  the  surface  sooner  than  does  bF' .  The  first  focal 
line  which  is  perpendicular  to  the  plane  of  the  paper,  is  at  F' .  On 
the  other  hand  the  rays  must  all  reach  the  axis  of  the  surface  at  the 
second  focal  line,  F"F"'. 

Astigmatism  of  the  human  eyeball  was  discovered  by  Thomas 
Young  in  the  year  1801.  He  proved  the  defect  in  his  own  eye  by 
means  of  his  optometer  and  also  by  observing  the  forms  of  circles  of 
diffusion  formed  by  a  luminous  point.  He  furthermore  proved  that 
the  astigmatism  in  his  own  eye  was  not  resident  in  the  cornea,  as  the 
amount  was  not  altered  by  immersing  his  eye  under  water,  and  sub- 
stituting a  spherical  lens  for  the  cornea.  He  thought  that  his  astig- 
matism was  due  to  an  obliquity  of  the  crystalline  lens  and  remarks 


254  THE   EYE.    ITS   REFRACTION   AND   DISEASES. 

that  the  error  could  be  corrected  by  placing  a  spherical  lens  obliquely 
in  front  of  the  eye. 

Airy,  an  astronomer  and  professor  in  Cambridge,  was  the  jfirst  to 
correct  astigmatism  by  the  use  of  cylindrical  lenses.  Donders  was 
the  first  to  have  cylindricals  put  in  the  test  cases,  A  luminous  point 
was  at  first  used  to  detect  the  principal  meridians  and  then  a  steno- 
paic  slit  used,  and  the  refraction  measured  separately  in  the  two 
meridians;  later  Javal  introduced  the  method  of  using  the  star-figure 
and  the  cylinders  in  applying  the  test  and  correcting  astigmatism. 

The  thing  to  do  with  cases  of  irregular  astigmatism  is  to  study 
them  carefully,  and  correct  the  regular  part  of  the  ametropia,  and 
thus  bring  vision  up  as  much  as  possible.  It  may  be  supposed  that 
if  the  meridians  of  the  greatest  and  the  least  refraction  of  an  eye  with 
irregular  astigmatism  were  not  at  right  angles  to  each  other  that  the 
case  may  be  corrected  by  the  use  of  crossed  cylindrical  lenses  with 
their  axes  inclined  towards  each  other,  but  this  is  not  the  case,  for 
the  meridians  of  the  greatest  and  the  least  refraction  are  always  at 
right  angles  to  each  other  no  matter  what  the  deviation  of  the  axes 
of  two  combined  cylinders.  If  they  are  of  equal  strength  and  of  same 
sign,  the  meridian  of  the  greatest  refraction  equally  divides  the  angle 
between  the  active  planes  of  the  two  cylinders,  and. the  meridian  of 
the  least  refraction  equally  divides  the  angle  between  the  axes  of  the 
cylinders.  If  the  combined  cylinders  are  unequal  but  of  the  same 
sign,  the  meridian  of  the  greatest  refraction  is  deviated  towards  the 
active  plane  of  the  stronger  cylinder,  and  the  meridian  of  the  least 
refraction  towards  the  axial  plane  of  the  same  cylinder.  If  the 
cylinders  are  equal  in  strength  but  of  contrary  signs,  the  meridian 
of  the  greatest  positive  refraction  equally  divides  the  angles  between 
the  active  plane  of  the  convex  and  the  axial  plane  of  the  concave 
cylinder  and  the  plane  of  the  greatest  negative  refraction  equally 
divides  the  angle  between  the  active  plane  of  the  concave  and  the 
axial  plane  of  the  convex  cylinder.  If  the  convex  cylinder  in  the 
combination  is  the  stronger,  the  meridian  of  the  greatest  positive  re- 
fraction is  deviated  towards  the  active  plane  of  the  convex  cylinder, 


ABNORMAL    RFFRACTION.  25'^• 

while  if  the  concave  cyUnder  is  the  stronger,  the  meridian  of  the 
greatest  negative  refractive  will  be  deviated  towards  the  active  plane 
of  the  concave  cylinder  of  the  combination. 

There  are  no  short  rules  for  ascertaining  the  sphero-cylindrical 
equivalent  of  crossed  cylindricals,  with  varying  incHnation  of  their 
axes.  It  is  just  as  well  to  neutralize  the  combination  with  trial 
lenses,  holding  the  cylinders  so  that  they  do  not  slip  from  their 
proper  positions  in  regard  to  each  other.  A  slight  slipping  will  make  ' 
it  impossible  to  properiy  neutralize.  Opticians  are  in  the  habit  of 
cementing  the  two  crossed  cylindrical  lenses  together,  before  trying 
to  neutralize,  when  searching  for  the  equivalent  sphero-cylindrical 
lens. 

In  some  cases  where  lenses  fail  to  improve  the  vision  at  all  or  to  a 
slight  amount  only,  stenopaic  spectacles  are  of  great  service.  Sten- 
opaic  spectacles  are  those  in  which  the  lenses  are  replaced  by  oqaque 
discs,  perforated  by  a  slit  running  in  the  preferred  direction  (nearest 
emmetropic),  or  more  commonly  perforated  by  a  pinhole,  through 
which  the  patient  sees.  The  slit  excludes  all  meridians  of  the  eye- 
ball from  the  visual  act  save  that  which  is  parallel  to  its  course.  A 
lens  may  be  combined  to  render  the  eye  emmetropic  in  the  latter 
meridian.  The  pinhole  acts  by  excluding  from  the  eye  all  light  that 
would  enter  save  through  a  definite  small  part  of  the  cornea  that  has 
little  astigmatism  on  account  of  its  size,  and  furthermore  the  small 
opening  limits  the  size  of  diffusion  circles  and  thus  renders  more 
accurate  the  focusing  of  all  external  objects.  A  lens,  convex  or  con- 
cave as  the  case  may  be,  placed  before  the  opening  may  improve  the 
vision  by  further  diminishing  the  size  of  diffusion  areas.  Stenopaic 
spectacles  are  objected  to  upon  the  ground  that  they  limit  the  field 
of  vision,  but  it  often  happens  that  a  man  or  woman  cannot  see  well 
enough  to  make  a  living  without  them.  The  curtailment  of  the  field 
is  lessened  and  one  is  enabled  to  see  to  the  side  without  turning  the 
head  so  much,  by  employing  discs  that  are  perforated  in  several 
places,  instead  of  only  at  the  center.  The  several  perforations  should , 
be  far  enough  apart  so  that  no  two  of  them  fall  within  the  pupillary 


256 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


area  at  the  same  time.  The  stenopaic  spectacles  shown  in  the  cut 
are  those  designed  by  Dr.  Heilbron,  and  are  claimed  to  be  of  great 
service  in  cases  of  very  high  myopia,  in  which  the  vision  can  not  be 
materially  improved  by  the  use  of  concave  spherical  lenses.  The 
perforations  are  too  close  together  and  as  a  rule,  they  are  of  little 
value.     The  vision  is  not  materially  improved  by  them. 


The  star  figure  used  in  detecting  astigmatism  affords  information 
only  on  the  astigmatism  that  can  be  corrected  by  cylindricals,  but  the 
form  under  which  a  luminous  point  is  seen  (the  manner  of  detecting 
regular  astigmatism  in  the  beginning)  furnishes  fuller  information. 
The  opening  in  the  light  shade  or  source  of  light 'should  be  .2-3 
mm.  in  diameter.  There  is  no  optical  defect  that  does  not  have  its 
especial  figure  caused  by  distortion  of  the  luminous  point.  No  two 
eyes  see  a  luminous  point  exactly  alike.  The  same  individual  sees 
it  different  with  the  two  eyes  unless  they  are  exactly  equal  in  refrac- 
tion. The  form  of  light  area  upon  the  retina  being  so  varied  in  dif- 
ferent eyes  and  at  different  distances  renders  it  practically  impossible 
to  properly  interpret  the  figure,  but  they  can  be  analyzed  to  a  certain 
extent.  The  following  are  the  rules  of  analysis  taken  from  Tschern- 
ing : 

1.  We  can  always  decide  whether  a  part  of  the  figure  is  formed 
by  crossed  rays  or  not,  by  covering  a  part  of  the  pupil.  If  it  is  the 
homonymous  part  of  the  figure  which  disappears,  this  part  is  formed 


ABNORMAL   REFRACTION. 


257 


by  rays  which  have  already  crossed  the  axis  before  reaching  the 
retina,  or  if  it  is  the  heteronymous  part  of  the  figure  which  disap- 
pears, the  rays  have  not  yet  crossed  the  axis. 

2.  If  the  luminous  point  is  beyond  the  punctum  remotum,  and  if 
the  observer  notices  a  concentric  brightness  on  a  part  of  the  diffusion 
spot,  this  part  corresponds  to  a  less  refracting  part  than  in  the  re- 
mainder of  the  pupil,  for  the  focus  of  this  part  is  nearer  the  redna 
and  its  rays  are  therefore  less  dispersed. 

3.  If  within  the  focus,  the  figures  are  elongated  in  one  direction, 
and  in  the  same  direction  beyond  the  focus,  the  eye  is  more  refract 
ing  in  this  direction. 

4.  The  aberroscopic  phenomenon  always  tells  us  in  what  direction 
the  refraction  increases  or  diminishes,  starting  from  the  center  of  the 
pupil,  and  finally  the  optometer  of  Young  permits  a  very  exact  study 
of  these  phenomena.  For  further  consideration  of  this  subject  of 
luminous  point  and  irregular  astigmatism  the  reader  is  referred  to 
Tscherning's  "Physiological  Optics." 

As  yet  we  know  of  no  way  of  correcting  irregular  astigmatism  by 
glasses.  The  method  of  Sulzer  of  applying  glasses  in  contact  with 
the  cornea  would  correct  most  of  the  error  if  resident  in  the  cornea^ 
but  the  cornea  will  not  tolerate  such  abuse.  Other  contact  glasses 
have  been  made  with  rims  to  be  supported  upon  the  sclera,  but  they 
likewise  seem  to  cause  much  annoyance. 

Anisometropia.  —  Anisometropia  means  an  unequal  refraction  in 
the  two  eyes.  It  is  rather  the  rule  in  eyes.  Frequently  it  is  of  a 
different  variety  as  well  as  of  degree  in  the  two  eyes,  thus,  myopia 
in  the  one  and  hyperopia  in  the  other.  The  importance  of  this  dif- 
ference in  refraction  depends  entirely  upon  the  degree  and  not  upon 
the  difference  in  the  kind  of  ametropia  in  the  two  eyes.  We  follow 
the  general  rule  to  correct  each  eye  and  to  prescribe  for  it  its  proper 
lens  unless  the  anisometropia  is  too  great.  If  the  difference  in  the 
refraction  of  the  two  eyes  is  over  four  or  five  diopters,  it  is  seldom 
that  the  patient  can  wear  with  any  degree  of  comfort  the  correcting 
lens  of  each  eye. 
17 


258  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

The  correcting  lenses,  besides  altering  the  position  of  the  foci, 
affect  the  size  of  the  retinal  images,  so  that  if  these  images  are  not 
of  nearly  the  same  size  the  brain  cannot  fuse  the  images  into  a  single 
ocular  perception,  but  there  will  exist  a  diplopia,  caused  by  the  super- 
imposition  of  the  projected  retinal  image  of  one  eye  upon  that  of  the 
other.  Bearing  this  fact  in  mind  the  refractionist  should  always  place 
the  spectacle  lenses  as  near  to  the  anterior  focal  point  of  the  eye  as 
possible  so  that  the  size  of  the  retinal  images  will  be  influenced  as 
little  as  possible  by  the  lenses,  in  high  degrees  of  anisometropia. 
If  the  optical  center  of  the  correcting  lens  coincides  with  the  anterior 
focal  point  of  the  eyeball,  the  retinal  image  is  always  the  same  size 
no  matter  what  the  ametropia  may  be,  for  the  rays  from  the  extremi- 
ties of  the  object  pass  into  the  eye- 
\^  V~l  /^""^  ^""N.        ball  without  deviation  and  are  par- 

^\^  I  \q^/\  \    allel  after  refraction  by  the  diop- 

^!^^<^  (    I  I   trie  system  of  the  eye,  so  that  the 

^y^    / 1    ^vJ /    retinal  image  is  always  the  same 

/   \  \^    ^y/      size  no  matter  what  the  distance  of 

retina  (figure). 

If  the  correcting  lens  is  placed  in  front  of  the  anterior  focus  of  the 
eyeball  the  retinal  image  of  the  myopic  eye  is  smaller  and  that  of 
the  hyperopic  eye  larger  than  that  of  the  emmetropic,  which  is  seen 
by  constructing  a  figure  analogous  to  the  one  above.  First  con- 
struct the  image  formed  by  the  lens  and  then  connect  the  extrem- 
ities of  the  image  with  the  anterior  focus  of  the  eyeball.  Patients 
often  claim  that  concave  glasses  diminish  objects  ;  this  may  be  due 
to  the  glass  being  placed  anterior  to  the  anterior  focus  of  the  eyeball 
or  to  the  fact  that  objects  seen  more  distinctly  appear  smaller,  be- 
cause there  are  no  longer  any  diffusion  circles  formed.  If  the  glass 
is  too  strong  the  patient  uses  his  accommodation  and  then  the  an- 
terior focus  of  the  eyeball  approaches  the  cornea  and  the  images  be- 
come smaller  for  that  reason.  However  a  very  few  individuals  pre- 
fer to  have  the  full  amount  of  their  anisometropia  corrected  when 
high  because  it  is  impossible  to  maintain  the  correcting  lenses  at  the 
anterior  focal  point  of  the  eyeball. 


ABNORMAL   REFRACTION. 


259 


Anisometropia  in  the  young  is  very  liable  to  give  rise  to  squint. 
In  some  cases  one  can  correct  one  eye  for  distant  seeing  and  the 
other  one  for  near  seeing.  Under  such  conditions  a  person  soon 
learns  to  use  the  eyes  alternately.  If  both  eyes  cannot  be  used  to- 
gether after  their  respective  correcting  lenses  are  adjusted,  it  is  the 
rule  to  correct  the  better  seeing  eye,  allowing  the  worse  eye  its  full 
correction  of  astigmatism,  with  a  sphere  equal  to  the  spherical  cor- 
rection of  the  other  eye.  To  decide  whether  one  sees  as  well  with 
the  proper  correction  before  each  eye  as  he  does  when  the  whole 
amount  of  the  ametropia  is  corrected  the  stereoscope  may  be  used. 
If  the  patient  fuses  well  with  the  correcting  lenses  on,  he  will  have 
little  trouble  to  adapt  his  eyes  to  them.  Another  way  is  to  alter- 
nately cover  the  poor  eye,  and  ask  the  patient  whether  he  sees  dis- 
tant and  near  printed  matter  better  when  the  eye  is  closed  or  not. 
Anisometropia  that  is  caused  by  the  unequal  change  in  refraction  of 
the  two  eyes  as  in  cases  of  progressing  myopia,  is  more  troublesome 
than  any  other  variety.  The  anisometropia  caused  by  illy  fitting 
spectacles  or  nose-glasses  is  likewise  very  annoying. 

Schulin  finds  that  as  a  rule  in  cases  of  anisometropia  the  right 
eye  has  less  hyperopia  or  more  myopia  than  the  left  one.  As  most 
people  are  right-handed,  and  have  a  tendency  to  use  the  right  eye 
more  than  the  left  one,  one  becomes  impressed  with  the  idea  that 
anisometropia  has  some  bearing  upon  the  use  of  the  eyes.  The  high 
degree  of  anisometropia  produced  by  the  extraction  of  the  crystalline 
lens  from  one  eyeball  should  not  be  corrected  by  spectacles,  as  the 
eye  without  its  lens  receives  the  larger  retinal  images  and  it  is 
rarely  that  an  individual  can  fuse  images  differing  so  much  in  size. 
As  the  anterior  focal  point  is  dislocated  about  i  cm.  further  anterior 
by  removal  of  crystalHne  lens  it  is  impossible  to  wear  the  correcting 
lens  at  the  anterior  focus  of  the  aphakic  eyeball.  The  distant  vision, 
especially,  will  be  found  to  be  much  better  with  the  aphakic  eye  un- 
corrected. The  patient  will  prefer  monocular  clear  vision  to  binocu- 
lar blurred  vision,  and  perhaps  diplopia. 


CHAPTER   XIX 


PRESBYOPIA 


Presbyopia.  —  The  power  of  accommodation  decreases  with  in- 
creasing years.  This  diminution  is  manifested  by  the  gradual  reces- 
sion of  the  near  point  of  accommodation.  The  decrease  in  the  power 
of  accommodation  can  not  be  referred  to  loss  of  strength  of  the 
ciliary  muscle,  due  to  senile  changes,  as  the  power  of  accommoda- 
tion begins  to  wane  in  childhood,  when  other  muscles  are  gaining  in 
strength.  The  cause  of  the  failure  of  accommodation  lies  in  the 
gradual  loss  of  elasticity  of  the  fibers  of  the  crystalline  lens,  due  to  a 
loss  of  water  or  process  of  sclerosis,  that  begins  centrally  and  extends 
gradually  to  the  surface  of  the  lens.  The  lens  becomes  harder  and 
harder  and  does  not  respond  to  the  relaxation  of  pressure  upon  it, 
through  the  suspensory  ligament  being  slackened  by  the  contraction 
of  the  ciliary  muscle,  by  bulging  forward  and  becoming  more  con- 
vex. This  loss  of  accommodation  does  not  become  troublesome 
until  the  near-point  has  receded  beyond  the  poipt  of  convenient 
near-seeing. 

The  man  who  holds  small  objects  close  to  the  eyes  is  the  one 
that  will  notice  failure  of  accommodation  first,  for  example  a  watch- 
maker or  typesetter.  As  the  loss  of  accommodation  is  a  gradual 
process,  the  time  when  presbyopia  sets  in  must  be  arbitrarily  estab- 
lished. 

The  amount  of  accommodation  diminishes  in  a  very  regular  man- 
ner with  age,  so  much  so  that  after  the  twenty-fifth  year  it  is  possible 
to  determine  the  age  of  the  individual  within  a  few  years  according 
to  the  amount  of  accommodation  he  possesses. 

Donders  assumed  that  presbyopia  begins  when  the  near-point  re- 
cedes beyond  22  cm.  (Jaeger  says  25  cm.)  when  the  amplitude  of 
accommodation  is  equal  to  4.50  D.  (100/22  =  4.50  D.).    This  occurs 

260 


PRESBYOPIA.  261 

in  the  majority  of  eyes  at  the  fortieth  year.  After  this  age  readino-  is 
laborious  and  glasses  are  needed  for  near  work. 

If  an  individual  reads  fine  print  without  glasses  when  over  fifty 
years  of  age  he  must  be  myopic  if  the  pupil  is  of  ordinary  size. 

Presbyopia  comes  to  all  eyes,  setting  in  sooner  in  the  hyperope 
than  in  the  myope,  as  the  former  needs  more  accommodation  than 
the  emmetrope  for  a  given  distance  and  is  therefore  quicker  to  ap- 
preciate any  loss  of  it,  while  the  myope  needing  less  accommodation 
than  the  emmetrope  is  not  so  soon  hampered  by  the  failure  of  it. 
People  with  presbyopia  avoid  reading  fine  print  and  hold  their  read- 
ing matter  at  a  great  distance  from  the  eyes.  They  often  find  that 
they  can  read  better  if  they  sit  with  their  faces  towards  the  light.  The 
reason  for  this  is  that  the  light  shining  into  the  eyes  contracts  the 
pupils,  and  as  the  size  of  the  diffusion  circles  is  thus  lessened,  there 
is  less  blurring  of  the  retinal  picture.  The  physiological  diminution 
of  the  pupil  incident  to  old  age  in  the  same  way  partially  corrects 
presbyopia. 

The  vision  of  the  presbyope  can  be  made  materially  better  by  read- 
ing through  a  pinhole  in  a  card  held  before  the  eye,  by  lessening  the 
size  of  diffusion  circles.  The  presbyopic  patient  does  not  experience 
pain  in  the  use  of  the  eyes  as  does  the  hyperope.  He  will  notice 
that  he  can  read  very  well  for  a  short  time,  but  that  the  print  then 
becomes  blurred.  If  the  eyes  are  closed  or  rested  for  a  short  while 
the  sight  again  comes  up. 

This  is  explained  by  the  fatigue  and  consequent  relaxation  of  the 
ciliary  muscle  in  its  effort  to  influence  the  sclerosed  lens.  Presbyopia 
demands  the  use  of  convex  spherical  lenses  for  near  work.  They 
must  be  of  the  strength  to  make  the  near  point  of  accommodation 
occupy  the  place  demanded  by  the  particular  kind  of  work  the  patient 
wishes  to  do  with  his  eyes.  The  manner  in  which  convex  spherical 
lenses  correct  presbyopia  is  shown  in  the  figure. 

Rays  r  and  r'  are  parallel  and  are  focused  without  accommodation 
upon  the  retina.  The  lens  is  omitted  for  simplicity  without  in  any 
deo-ree  alterino-  the  conditions.     Suppose  that  the  eyeball  did  not 


262  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

alter  its  refraction,  that  is,  the  crystalline  lens  did  not  change  its 
shape  as  the  eye  looked  at  point  O.  The  rays  from  the  near  point 
O  would  then  not  be  focused,  but  form  a  diffusion  area  upon  the 


retina  and  the  point  O  would  be  seen  indistinctly.  The  conjugate 
focal  point  of  O  is  behind  the  retina  at  O'.  The  convex  lens  L 
causes  the  light  from  point  O  to  emerge  from  it  in  plane  waves,  for 
which  the  eyeball  is  adjusted  when  at  rest,  and  therefore  the  point  O 
by  aid  of  the  lens  L  is  seen  distinctly.  In  the  figure  the  eye  is  repre- 
sented as  using  no  accommodation  at  all  when  it  directs  itself  to  the 
near-by  point,  and  therefore  the  lens  L  has  a  focal  interval  equal  to 
the  distance  of  the  point  O  from  its  optical  center.  If  the  eyeball  is 
capable  of  some  accommodation,  the  strength  of  L  must  be  decreased 
by  that  amount.  So  first  in  correcting  presbyopia  we  always  find  out 
how  much  accommodative  power  the  eye  has  left.  ,  Always  correct 
the  error  of  refraction  before  testing  for  presbyopia. 

Presbyopia  and  hyperopia  should  not  be  confounded  because  in 
each  the  near  point  of  accommodation  is  further  off  than  in  em- 
metropia. 

Ciliary  or  accommodative  asthenia  also  simulates  presbyopia.  It 
occurs  however  in  folks  under  forty  years  of  age.  It  is  due  to  in- 
herent weakness  of  the  ciliary  muscle,  or  occasioned  by  exhausting 
diseases,  or  by  paralysis  of  the  ciliary  muscle.  It  is  quite  the  rule  in 
the  higher  grades  of  myopia  to  find  an  inherent  weakness  of  the 
ciliar}'^  muscle.  Ciliary  asthenia  is  corrected  in  the  same  manner  as 
presbyopia  with  convex  spheres.  Exercise  of  the  ciliary  muscle  with 
the  internal  administration  of  strychnine  will  develop  it  if  not  paretic 
in  origin.     This  is  especially  true  in  myopia.     Exercise  is  carried  on 


PRESBYOPIA.  263 

by  reading  for  awhile  daily  with  a  pair  of  weak  concave  spheres 
which  in  cases  of  myopia  should  be  slighdy  stronger  than  those 
needed  for  reading.  Paralysis  of  the  ciliary  muscle  will  be  considered 
under  the  head  of  paralysis  of  the  ocular  muscles. 

With  the  recession  of  the  near  point  there  is  a  series  of  recurrent 
weaknesses  of  the  extra-ocular  muscles.  This  is  best  seen  in 
monocular  adduction,  and  during  convergence.  The  weakness  of 
the  muscles  is  not  corrected  by  the  glasses  that  correct  the  error  of 
focusing.  For  this  reason  it  at  times  happens  that  weak  prisms  are 
needed  (bases  in)  in  addition  to  the  convex  spheres  for  the  correction 
of  presbyopia. 


CHAPTER   XX 

MUSCULAR    INEFFICIENCY 

Balance  of  the  Extra-ocular  Muscles.  —  Under  normal  conditions 
when  the  eyes  are  in  the  primary  position,  there  is  no  tendency  to 
depart  therefrom.  When  adjusted  for  an  object  at  a  distance  of 
twenty  feet  or  beyond,  the  eyes  should  be  passively  directed.  There 
should  be  no  action  or  contraction  of  any  extra-ocular  muscle,  to 
maintain  the  eyeballs  in  their  proper  direction.  All  antagonistic 
muscles  should  be  at  rest  and  equally  balanced  in  regard  to  their 
tension  upon  the  eyeballs.  This  ideal  condition  of  the  extra-ocular 
muscles  is  spoken  of  as  orthophoria  {6p06<;,  straight,  and  ^epetv,  to 
bear  or  sustain).  Any  tendency  on  the  part  of  one  eye  or  both  to 
turn  away  from  the  object  of  attention,  being  held  in  the  right  posi- 
tion only  by  an  excessive  amount  of  innervation  to  the  weaker  of  the 
opposing  muscles,  constitutes  heterophoria  [erepo^,  different,  and 
(fyepetv,  a  bearing  or  tending  in  some  other  way  than  the  normal).  It 
is  also  spoken  of  as  muscle  imbalance,  muscular  inefficiency  or  in- 
sufficiency, or  muscular  asthenopia.  The  two  eyes  are  kept  properly 
directed  by  what  is  known  as  the  guiding  sensation,  which  is  nothing 
more  than  the  effort  on  the  part  of  the  eyes  to  have  single  binocular 
vision.  The  abhorrence  of  diplopia  is  so  great  that  if  one  eye 
actually  deviates  from  the  object  of  attention  the  brain  soon  learns 
not  to  take  account  of  the  image  formed  in  the  deviating  eye,  or 
as  we  say  suppresses  the  image  of  the  deviating  eye  (seen  in 
cases  of  squint).  There  may  be  a  tendency  to  deviate  on  the  part 
of  one  or  both  eyes,  but  if  each  eye  is  a  good  seeing  one  the  guid- 
ing sensation  will  cause  innervation  to  go  to  the  right  muscles  so 
that  the  eyes  will  be  properly  directed,  inasmuch  as  seeing  with 
both  eyes  is  preferable  when  both  are  good,  as  then  the  one  helps 
the  other. 

264 


MUSCULAR   INEFFICIENCY.  265 

Muscular  inefficiency  may  be  described  as  a  preponderance  of 
strength  of  one  muscle  or  a  set  of  muscles  over  their  antagonists 
within  the  limits  of  single  binocular  vision.  If  the  difference  in 
strength  is  too  great  to  be  habitually  overcome  by  nerve  innervation, 
the  stronger  muscles  gain  power  over  the  eyes  and  squint  results. 
Von  Graefe  described  muscle  imbalance  as  latent  squint  or  strabismus 
(dynamic  squint)  ;  imbalance  of  the  extra-ocular  muscles  is  rather 
common.  It  is  at  times  caused  by  refraction  errors  and  disappears 
when  the  latter  are  corrected.  Such  are  called  pseudo-inefficiencies. 
The  lack  of  balance  may  be  due  to  the  weakness  of  one  muscle 
(asthenic  heterophoria)  or  to  the  excessive  strength  of  its  antagonist 
(sthenic  heterophoria).  If  binocular  single  vision  ceases  to  exist 
through  the  loss  of  sight  of  one  eye,  or  if  binocular  diplopia  is  pro- 
duced by  some  artificial  means,  the  guiding  sensation  ceases  to  act, 
and  each  eyeball  rotates  in  the  direction  that  its  strongest  acting 
muscle  pulls  it.  Under  these  conditions  the  strain  upon  the  nervous 
system  to  keep  the  eyes  properly  directed  is  useless,  as  monocular 
vision  is  all  that  can  be  obtained,  so  the  guiding  sensation  ceases  to 
operate,  and  thus  reserves  nervous  energy  for  other  functions. 

If  there  is  a  tendency  for  the  visual  axes  to  deviate  inwards,  that  is 
in  convergence,  we  speak  of  it  as  esophoria  (from  ©rw,  in,  and  <f)epei,j/, 
to  bear  or  tend),  and  when  the  eyes  tend  to  deviate  outwards, 
exophoria  (from  e$,  out,  and  <^e/3eti/,  to  bear  or  tend).  If  either  eye 
tends  to  deviate  upwards,  or  its  fellow  downwards,  we  call  it  right  or 
left  hyperphoria  {vTrep,  above,  and  <l)4p€Lv),  according  to  which  eyeball, 
the  right  or  left,  has  the  tendency  to  elevate.  If  both  optic  axes 
tend  to  rise  above  the  median  plane,  we  have  anaphoria  {avd,  up- 
ward, and  <j)€p€Lv),  and  if  there  is  a  tending  of  both  eyes  to  be 
depressed  below  the  median  plane,  cataphoria  (/caret,  down,  and 
(f)€peLv).  Each  eye  always  turns  from  the  weak  muscle  towards  the 
strong  one  ;  esophoria  therefore  means  a  weakness  of  the  external 
recti,  and  exophoria  of  the  interni.  Cyclophoria  {kvk\o<;,  circle,  and 
(jyepeLv)  is  the  term  employed  when  the  eyeballs  tend  to  undergo  tor- 
sion, or  when  the  oblique  muscles  are  insufficient  to  keep  the  vertical 


266  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

meridians  of  the  eyes  parallel  with  the  median  plane  of  the  head.  It 
is  spoken  of  as  plus  when  the  vertical  axes  of  the  eyes  have  a  ten- 
dency from  the  median  plane  of  the  head,  and  as  minus  when  they 
have  a  tendency  towards  the  median  plane  of  the  head  in  conformity 
with  the  terms  plus  and  minus  torsion,  used  by  Maddox. 

The  lack  of  muscular  equilibrium  may  be  evident  when  the  eyes 
are  adjusted  for  both  near  and  distant  seeing,  or  only  when  adjusted 
for  the  one  or  the  other.  There  are  several  possibilities  in  regard  to 
the  nature  of  heterophoria.  There  is  no  one  theory  that  will  hold  for 
all  cases.  One  view  is  that  there  is  a  congenital  feebleness  of  one 
muscle  as  compared  with  its  opposing  muscle  ;  the  weakness  being 
either  due  to  the  fewness  of  its  fibers  or  to  the  manner  of  its  inser- 
tion to  the  eyeball,  the  weak  muscle  being  abnormally  far  from  the 
corneo-scleral  junction,  or  again  to  the  lack  of  sufficient  innervation. 
Some  deny  that  heterophoria  is  ever  congenital ;  that  the  growth  of 
the  muscle  has  been  normal,  but  that  some  irritation  in  or  about  the 
eye,  or  in  some  distant  organ  of  the  body,  excites  a  spasm,  tonic  in 
its  nature,  in  one  of  a  pair  of  muscles,  thus  destroying  their  harmo- 
nious action.  A  few  cases  may  be  due  to  eccentricity  of  the  mac- 
ulae lutea,  that  is,  that  the  maculae  do  not  occupy  corresponding  places 
in  the  two  retinae. 

A  congenital  displacement  of  one  macula  in  or  out  will  give  rise  to 
eso-  or  exophoria.  This  latter  theory  includes  those  cases  produced 
by  a  faulty  position  of  the  eyes  in  the  orbits.  If  one  orbit  is  higher 
or  lower  than  the  other  one,  a  hyperphoria  will  be  the  result.  The 
last  theory  is  that  of  Dr.  Savage.  In  many  cases  there  is  esophoria 
for  distance  and  exophoria  for  near  seeing  at  variance  with  all  the 
theories.  There  is  a  condition  called  reversed  heterophoria.  This" 
is  where  the  eyes  have  a  tendency  to  turn  in  the  direction  of  the  in- 
herently weaker  muscles.  The  weak  muscles,  in  their  attempt  to  do 
their  work  of  maintaining  the  eyes  in  the  proper  positions,  have 
become  thrown  into  a  spasm.  Thus  there  may  be  a  true  exophoria 
(an  actual  preponderance  of  strength  of  the  external  recti),  yet  so 
great  is  the  effort  on  the  part  of  the  nerve  centers  to  overcome  its 


MUSCULAR   INEFFICIENCY.  267 

manifestation  that  an  excess  of  nerve  impulse  is  sent  to  the  interni, 
throwing  them  into  a  spasmodic  contraction  which  not  only  conceals 
the  exophoria,  but  actually  carries  the  eyes  so  far  inwards  that  the 
tests  reveal  an  esophoria. 


CHAPTER  XXI 

DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION 

It  is  essential  to  keep  an  accurate  record  of  each  ophthalmic 
patient,  so  that  any  change  from  time  to  time  may  be  accurately 
noted,  and  in  case  the  patient  loses  his  glasses,  they  can  then  be 
supplied  without  a  reexamination.  Records  are  best  kept,  according 
to  the  author's  opinion,  in  a  book.  After  taking  the  history  as  to 
how  the  patient  complains  and  so  on,  and  after  examining  the  eyes 
by  oblique  illumination  and  with  the  ophthalmoscope  for  any  diseased 
conditions  (which  should  always  be  done),  one  is  prepared  to  examine 
the  refraction.  The  fundus  of  the  eye  should  in  all  cases  be  care- 
fully examined,  even  if  vision  is  found  to  be  perfect,  as  it  not  infre- 
quently happens  that  the  vision  is  not  disturbed  when  there  is  a 
rather  advanced  lesion  of  the  fundus.  It  is  well,  therefore,  to  get 
into  the  habit  of  examining  the  fundi  of  the  eyes  before  proceeding  to 
refract  them.  In  all  cases  where  a  diseased  condition  is  found,  the 
refraction  error  should  be  corrected  if  there  is  any  reason  to  suppose 
whatever  from  the  nature  of  the  trouble  or  from  the  presence  of  re- 
curring attacks  or  what  not,  that  the  condition  depends  upon  eye- 
strain. 

Quite  a  few  folks  apply  to  have  their  eyes  tested  for  the  relief  of 
poor  vision,  when  there  is  an  intra-ocular  lesion  that  is  interfering 
with  the  seeing.  Therefore,  opticians  should  not  be  allowed  by  law 
to  test  eyes  for  glasses,  as  any  diseased  condition  of  the  eyes  would 
naturally  be  overlooked  by  them.  Some  of  the  more  conscientious 
of  them  will  refer  a  patient  to  an  oculist  if  he  finds  that  he  cannot 
bring  the  vision  up  to  normal  with  his  glasses,  but  they  are  few.  It 
is  necessary  in  the  majority  of  cases  to  have  the  eyes  under  the 
effect  of  a  cycloplegic  to  intelligently  test  and  properly  correct  the 
orror  of  refraction.     It  frequently  happens  that  accommodation  ren- 

268 


DETECTION    AND    CORRECTION   OF   ERRORS   OF    REFRACTION.     269 

ders  an  error  latent,  or  covers  it  up,  and  the  trouble  is  not  revealed 
without  the  use  of  a  cycloplegic.  Hyperopia  is  made  to  appear  less 
or  even  emmetropia,  or  again  converted  into  myopia  under  the  action 
of  the  ciliary  muscle.  The  eyes  should  in  most  cases  be  tested  while 
under  the  effect  of  a  cycloplegic,  and  then  retested  after  the  effect  of 
the  drug  has  worn  off,  and  the  proper  allowance  and  change  in  the 
strength  of  glasses  made  for  the  return  of  accommodation.  This  is 
especially  necessary  for  the  beginner  and  in  the  more  complicated 
cases  of  astigmatism,  as  mixed  and  compound  oblique. 

Again — with  mydriases  the  patient  may  use  some  other  part  of  the 
cornea  than  the  visual  zone,  so  that  when  the  pupil  returns  to  its  nor- 
mal size  the  glasses  are  unsatisfactory. 

Subjective  methods  depending  upon  the  goodwill  and  intelligence 
of  the  patient  are  of  course  inferior  to  objective  methods  of  examina- 
tion. The  latter,  however,  should  always  be  confirmed  by  the  former 
whenever  possible,  as  there  is  a  physiological  side  to  vision,  and  not 
entirely  of  an  optical  nature. 

For  example  there  is  a  certain  small  number  of  cases  of  objective 
astigmatism  that  are  not  comfortable  when  the  total  amount  of  the 
astigmatic  error  is  corrected,  there  being  present  an  unusual  amount 
of  physiological  astigmatism,  which  when  corrected  disturbs  the  phys- 
iological balance  or  the  new  conditions  imposed  upon  the  eyes  by 
fully  correcting  the  ametropia  annoy.  How  to  tell  these  cases  before- 
hand I  am  not  certain.  It  is  said  that  physiological  astigmatism  does 
not  disturb  vision  to  the  same  extent  as  pathologic.  Physiological 
astigmatism  is  certainly  overestimated  by  the  foreign  ophthalmologists. 
It  seems  to  me  that  it  should  always  be  placed  as  low  as  or  less  than 
.50  D.  In  a  series  of  cases  of  astigmatism  tabulated  several  years 
ago  by  Dr.  Julian  J.  Chisolm,  embracing  about  two  thousand  cases 
in  all,  it  was  found  that  a  .25  D.  and  a  .50  D.  of  error  seemed  to 
give  rise  to  the  most  annoyance,  other  than  faulty  vision.  The  dif- 
ference in  the  strength  of  the  cylinder  accepted  under  the  fogging 
test  (see  Fogging  Test),  and  that  required  to  correct  the  astigma- 
tism after  the  convex  sphere  has  been  removed  in  many  cases  is 


270 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


due  probably  to  physiological  astigmatism.  In  the  majority  of 
cases  glasses  do  not  prove  satisfactory  at  once,  but  there  is  a  vary- 
ing period  of  adaptation,  lasting  from  a  few  days  to  as  much  as 
several  weeks.  The  patient  should  be  informed  of  this  fact  so  that 
he  does  not  suppose  that  the  glasses  are  at  fault,  if  he  does  not  see 
as  well  at  first  with  them  on  as  he  does  with  them  off ;  which  will 
happen  in  cases  of  hyperopia,  or  if  his  eye-strain  does  not  immediately 
disappear.  The  quickest  way  to  become  accustomed  to  glasses  is  to 
wear  them  constantly  from  the  first.  The  objection  often  raised  to 
the  use  of  cycloplegics  that  it  takes  time,  for  while  the  effect  of  the 
drug  lasts  the  patient  is  compelled  to  do  without  the  use  of  his  eyes, 
is  overcome  in  a  great  measure  by  the  use  of  the  following  solution  : 


Homatropin  hydrobromate 

Cocain  muriate, 

Water, 


1 


aa  gr.  1. 

dr.  ii.     M. 


Two  or  three  drops  are  instilled  into  the  eyes  every  ten  minutes 
for  a  period  of  two  hours  previous  to  examination.  The  effect  of 
this  solution  mostly  wears  off  in  twelve  hours,  and  always  in  twenty- 
four  hours.  At  times  however  this  solution  is  not  strong  enough  to 
completely  relax  the  ciliary  muscle,  and  a  solution  of  atropine  gr.  4  to 
oz.  I,  has  to  be  used  for  several  days.  Below  is  found  a  table  show- 
ing the  various  strengths  of  the  several  mydriatics  and  cycloplegics 
in  use,  and  the  duration  of  their  action  upon  the  ciliary  muscle  and 
so  forth. 


TABLE    OF    MYDRIATICS. 


Name  of  Drug,  and  the  Salt 
Commonly  Used, 

Relative  Power 

in  Same  Strength 

Solution. 

Strength  of 

Solution 

Commonly 

Used. 

Time  when 

Solution 

Produces 

Effect. 

Period  of 

Maximum 

Effect. 

Effect 
Begins  to 
Decline. 

Complete 
Recovery. 

Atropin  Sulphate. 
Daturin         " 
Hyoscyamin" 
Duboisin       '* 
Scopolamin  muriate. 
Homatropin  hydrobromate. 
Cocain  muriate. 

30 
60 

75 

75 

75 

I 

not  comparable. 

I  :  120 
I  :200 
I  :240 
I  :  240 
I  :  1000 
I  :40 
1:125 

12  min. 
10     " 

15     ]' 
30     " 

I  hour. 
40  min. 

I  hour. 

4  days. 

1  <( 
0 

2  " 
(<      << 

12  hours. 

3  " 
2     <' 

15  days. 
10    " 
8     " 
i(      <( 

6     " 

2     " 
1 2  hours. 

DETECTION   AND   CORRECTION   OF   ERRORS   OF   REFRACTION.     27 1 

Euphthalmin  is  a  new  mydriatic  claimed  by  many  to  be  devoid  of 
any  effect  upon  the  ciliary  muscle.  The  salt  used  is  the  muriate,  in 
2-5  per  cent,  solution.  A  5  per  cent,  solution  will  dilate  the  pupil 
fully  in  from  20  to  30  minutes.  Hinshelwood  says  a  5  per  cent,  solu- 
tion produces  a  paresis  of  accommodation  that  lasts  about  two  hours. 
All  mydriatics  affect  to  some  extent  the  ciliary  muscle,  cocain  and 
euphthalmin  to  the  least  extent.  When  a  drug  has  put  the  accom- 
modation in  abeyance,  the  pupil  is  dilated  fully,  unless  held  by  ad- 
hesions to  the  crystalline  lens,  and  the  patient  is  unable  to  read  or  to 
see  small  objects  close  by.  With  the  rod  optometer  he  will  be  unable 
to  see  the  finest  print  save  at  the  ten-inch  point.  Often  when  the 
eye  is  fully  under  the  effect  of  the  medicament,  there  is  noticeable  a 
circumcorneal  injection  due  to  the  blood  being  pushed  out  of  the  iris 
into  the  circumcorneal  loops  of  blood-vessels.  This  is  particularly 
the  case  after  the  use  of  homatropin. 

SUBJECTIVE    TESTING. 

The  Trial  Case.  — The  case  of  test  lenses  represented  below  con- 
tains 35  pairs  of  convex  and  concave  spherical  lenses  ranging  from 
.  1 25  D.  to  20  D.,  and  23  pairs  of  convex  and  concave  cylindrical  lenses 
ranging  from  .125  D.  to  6  D.,  thirteen  prisms,  from. 5  to  20  degrees, 
four  plain  colored  glasses  ;  one  white  glass  ;  one  half-ground  glass  ; 
two  metal  discs,  with  stenopaic  slit ;  one  stenopaic  disc  with  hole ; 
one  solid  metal  disc,  and  two  pairs  of  trial  frames,  one  with  revolving 

cells. 

The  usual  arrangement  of  the  contents  of  the  trial  case  is  as  shown 
in  the  cut.  The  convex  lenses  are  to  be  found  in  the  right  half  of 
the  case  and  the  concave  in  the  left  half  Upon  the  partition  sepa- 
rating the  lenses  of  each  pair  is  marked  the  strength  of  the  glass  in 
the  adjoining  space.  The  numerations  are  usually  in  both  the  inch 
and  dioptric  system  ;  the  former  to  the  right,  and  the  equivalent  num- 
ber of  diopters  in  the  left-hand  column. 

The  General  Plan  of  Procediire.—lX.  is  well  to  have  some  definite 
order  in  testing  eyes  for  glasses,  and  then  nothing  will  be  overiooked. 


272 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


The  following  routine  is  that  used  by  the  author :  (i)  Estimation  of 
vision  ;  (2)  employment  of  oblique  illumination  ;  (3)  ophthalmoscopic 
examination  ;  (4)  optometry  ;  (5)  ophthalmometry;  (6)  muscle  balance 
tests  ;  (7)  retinoscopy  without  cycloplegic,  as  an  aid  for  subjective 
test  with  trial  case  ;  (8)  confirmation  subjectively  with  trial  case.  If 
vision  is  not  brought  to  normal,  or  if  there  is  any  disagreement  be- 
tween the  objective  and  the   subjective  tests,  a  cycloplegic  is  pre- 


scribed and  on  a  subsequent  day,  the  shadow  test  employed  and 
confirmed  by  the  trial  case.  For  the  methods  of  applying  these  tests, 
consult  the  articles  upon  them,  respectively. 

The  vision  of  both  eyes  together  and  then  of  each  eye  separately 
is  to  be  tested.  There  are  many  that  will  not  see  better  than  20/30 
with  either  eye,  but  will  have  20/20  or  better  with  both  eyes  open. 
Placing  the  opaque  disc  before  one  eye  seems  to  interfere  with  the 


DETECTION   AND    CORRECTION   OF   ERRORS   OF   REFRACTION.     273 

vision  of  the  uncovered  eye.  If  this  fact  had  not  been  taken  into 
account,  time  would  be  wasted  in  endeavoring  to  render  the  vision 
in  the  eye  under  test  normal.  The  near  point  of  distinct  vision 
should  then  be  ascertained  (with  or  without  the  rod  optometer). 

If  the  distant  vision  is  found  imperfect  place  a  stenopaic  disc  with 
a  hole  before  the  eye,  and  if  the  imperfection  in  vision  is  due  to  an 
error  of  refraction,  the  vision  will  be  improved.  If  the  poor  vision  is 
due  to  a  diseased  condition  or  congenital  defect  the  pinhole  disc  will 
not  improve  it  and  therefore  glasses  would  be  useless  as  far  as  the 
immediate  improvement  of  visual  acuity  is  concerned. 

Amblyopia  is  the  term  used  to  denote  poor  vision  without  any  dis- 
cernible cause  with  the  ophthalmoscope.  It  is  the  rule  in  the  higher 
errors  of  refraction  to  find  one  eye,  usually  the  one  with  the  higher 
error,  amblyopic.  This  is  at  times  due  to  faulty  development,  but  also 
ensues  from  non-use  (amblyopia  exanopsia).  Congenital  amblyopias 
have  vision  of  20/200  or  less  as  a  rule,  while  the  acquired  cases  have 
20/  100  or  better  with  the  refraction  correction.  Acquired  amblyopia 
is  usually  associated  with  squint  and  is  occasioned  by  the  suppression 
of  the  retinal  image  in  the  squinting  eye  to  avoid  diplopia.  In  cases 
where  the  eyes  are  straight,  the  image  of  one  eye  may  be  suppressed 
so  that  the  effort  for  binocular  vision  is  not  made — there  being  pres- 
ent an  anomaly  of  extra-ocular  muscles  which  renders  this  difficult. 
All  cases  of  amblyopias  should  be  corrected  accurately  by  some  ob- 
jective method,  and  the  proper  glass  worn  before  the  eye,  as  most 
of  them  improve  in  seeing  after  awhile  especially  if  the  vision  is 
20/100  or  better,  or  if  any  improvement  is  at  first  noted  with  the 
glasses.  Some  have  suggested  that  atropine  be  instilled  into  the 
good  eye  at  intervals  and  the  patient  made  to  depend  upon  the 
faulty  eye.  This  may  do  in  children  but  few  adults  are  willing  or 
able  to  be  so  afflicted. 

In  astigmatism  of  high  degrees  there  is  often  present  a  peculiar 
sort  of  amblyopia  or  inability  on  the  part  of  the  eye  to  see  lines 
drawn  in  certain  directions.  It  will  be  referred  to  under  the  head 
of  Astigmatism. 


274 


THE   EYE.    ITS    REFRACTION   AND    DISEASES. 


In  regular  ametropias,  the  pinhole  disc  usually  brings  the  vision 
up  to  about  the  same  point  as  correcting  lenses,  if  the  test-card  is 
well  illuminated.  In  irregular  astigmatism,  the  vision  is  often  made 
much  better  by  aid  of  the  hole  than  can  be  hoped  for  by  the  aid  of 
lenses.    In  astigmatism  the  visual  acuity  through  the  hole  is  not  quite 

as  good  as  in  cases  of 
hyperopia  or  myopia, 
as  notwithstanding  the 
small  area  of  cornea  ex- 
posed by  the  hole,  there 
is  still  enough  inequality 
in  curvature  to  distort 
the  retinal  images  to  a  degree.  The  higher  the  ametropia  the  larger 
the  diffusion  circles  upon  the  retina  and  the  poorer  the  vision.  The 
stenopaic  opening  lessens  the  size  of  the  diffusion  circles,  and  in  cases 
of  astigmatism  renders  them  more  circular,  and  thus  raises  the  visual 
acuity. 

a,  b,  r,  </  is  a  beam  of  light,  that  on  entering  the  eyeball  A  would 
be  brought  to  a  focus  at  the  point  /^  forming  a  diffusion  circle  the 
size  of  X  in  diameter. 
By  placing  the  pinhole 
disc  D  in  front  of  the 
eye,  all  rays  save  those 
passing  through  the 
central  opening  O  are 
excluded  from  the  eye- 
ball. All  entering  rays  must  then  fall  within  the  limits  of  c,  b,  and 
coming  to  a  focus  at  the  point  7^  a  diffusion  circle  is  formed  upon  the 
retina  the  size  of  y.  A  small  opening  also  magnifies  to  some  extent 
an  object  looked  at  through  it. 

In  both  figures  the  crystalline  lens  is  omitted  for  simplicity.  Let 
A  be  the  object,  and  a  its  retinal  image,  formed  by  lines  drawn 
through  the  nodal  point  N  from  extremities  of  object.  Z^  is  a  screen 
and  O  a  central  opening.     With  the  screen  interposed  the  light  that 


■-'v^^ 


DETECTION   AND   CORRECTION   OF   ERRORS   OF   REFRACTION.     275 

enters  the  eyeball  diverging  from  object  has  its  immediate  origin  at 
O.  The  size  of  image  through  O  is  1-2,  larger  than  a.  Rays  rr'  and 
ss\  being  divergent,  are  not  brought  to  a  focus,  until  the  points  V  V 
are  reached. 

As  has  been  said  it  is  better  to  refract  at  a  distance  of  twenty  feet 
or  more,  as  then  the  accommodation  does  not  so  readily  enter  in  to 
complicate  matters.  Just  as  good  work  can  be  done  at  less  distance 
if  allowance  is  made  for  the  shorter  distance  in  prescribing.  Many 
have  not  twenty  feet  at  their  disposal,  and  must  refract  at  less. 
There  are  test-cards  constructed  to  be  used  at  a  distance  of  twelve 
feet  or  four  meters,  a  very  convenient  distance. 

The  glass  that  is  correct  for  seeing  at  four  meters  is  of  course  .25 
D.  too  strong  if  it  is  a  convex  glass  and  .25  D.  too  weak  if  concave, 


^^ 

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for  greater  distances  than  four  meters.  Divide  the  distance  at  which 
the  refraction  work  is  done  into  one  meter  or  100  cm.,  and  ascertain 
the  amount  of  accommodation  employed  at  that  distance.  Thus, 
at  4  m.  distance  .25  D.  accommodation  is  used  (^  =  .25  D.).  To 
overcome  the  necessity  of  having  to  add  or  subtract  from  every  cor- 
rection, when  refracting  at  less  distance  than  twenty  feet  (at  twenty 
feet  the  amount  of  accommodation  used  is  so  little  that  it  is  ignored), 
Dr.  Forster  has  devised  some  reversed  test-types,  subtending  the 


276 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


correct  angle,  which  when  hung  above  the  head  of  the  patient  are 
seen  properly  in  a  mirror  hung  in  front.    The  distance  of  the  patient 

from  the  mirror  plus  that  from  the  test- 
type  to  the  mirror  is  made  equal  to  20 
^\  feet,  to  give  the  correct  test  for  distant 
vision  as  the  patient  looks  into  the  mir- 
ror. These  cards  are  shown  in  previous 
cut.  The  type  is  also  made  of  trans- 
lucent material  so  that  a  light  placed 
behind  them  will  illuminate  them  if  day- 
light is  not  available. 

Test-type  should  be  hung  at  the  height 
of  the  patient's  eyes.  The  most  conve- 
nient method  is  to  have  them  so  ar- 
ranged that  one  or  the  other  can  be 
shown  without  the  necessity  of  leaving 
one's  position  to  hang  another  card  up, 
and  as  the  patient  soon  learns  the  cards 
by  heart,  it  is  well  to  have  those  out  of 
use  out  of  sight  of  the  patient,  and  only 
exposed  as  needed.  This  is  accom- 
plished by  having  the  cards  enclosed 
within  a  wall  cabinet  and  lowered  before 
the  patient's  eyes  as  needed  by  means  of 
strings.  The  strings  are  passed  through 
screw  eyes,  and  attached  to  a  panel  be- 
side the  examiner.  To  avoid  the  neces- 
sity of  looking  at  the  cards  to  see  if  the 
patient  is  reading  properly,  one  has  a  number  of  tally  cards,  placed 
upon  the  panel,  under  the  strings  that  operate  the  respective  test- 
type.     The  accompanying  cut  shows  the  ophthalmic  cabinet. 

The  objection  to  the  ophthalmic  cabinet  is  that  all  the  cards  must 
be  of  the  same  size,  which  is  not  always  possible  with  different  style 
cards.     One  may  arrange  the  cards  in  the  same  manner  without  the 


r  2  B  D  E 

O  E  L  2  T  G 


DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION.  2/7 


cabinet,  and  use  any  size  card.  If  hung  close  enough  together  the 
cards  will  slide  smoothly  upon  one  another.  There  are  a  number  of 
good  test-card  brackets  and  stands  to  be  had  ;  several  of  the  best  are 
shown  in  the  cuts  below. 

Many  cards  may  be  hung  one  over  the  other.  The  cards  are 
always  in  place.  There  is  no  taking  down  or  hanging  up.  The 
cards  do  not  become  soiled,  bent  or  broken.     When  it  is  desired  to 


V 


E 


C  B 

DLN 

PTER 

FZBDE 

OriiCTG 

A  P  FO  R  E  0 
NPZL.RFDHLKI 

VCAHCPKST 


change  cards,  all  that  is  necessary  is  to  turn  the  upper  card  on  the 
rod  toward  the  left.  The  other  cut  shows  a  portable  stand  consist- 
ing of  an  upright  and  heavy  iron  base  carrying  an  adjustable  gas 
bracket  with  Argand  burner  and  mirror  reflector  in  combination, 
with  an  additional  arm  to  which  is  fastened  a  reversible  frame  con- 
taining two  cards  of  test-letters. 

If  an  individual  has  normal  or  nearly  normal  vision,  myopia  may 
be  excluded,  for  the  myopic  eye  can  not  help  itself,  by  accommodating 
(increased  convexity  of  the  crystalline  lens),  the  greater  refraction 
only  exaggerating  the  error. 


278 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


EVIDENCES    GAINED    FROM    THE    VISUAL   ACUITY. 


Distant  Vision. 

Emmetropia 

Hyperopia  may  be 

Myopia,  can  not  be 

Astigmatism,  if  not 

20/20  or  better. 

20/20  by  accom- 
modation but 
often  less. 

20/20. 

over  I  D.,  may 
be  20/20  by  ac- 
commodation. 

Near  Vision. 

Snellen,  1,5  in. 

Snellen,  No.  I  or 

Snellen,  i  or  2,  but 

Larger  print  only. 

to  20  in. 

larger  but  not 
close  up. 

not  as  far  off  as 
distance  noted. 

To  exclude  the  effect  of  astigmatism  over  visual  acuity  lines  run- 
ning in  the  direction  of  most  distinct  vision  may  be  used.  We  can 
exclude  all  influence  of  refractive  errors  by  placing  a  stenopaic  open- 
ing before  the  eye  under  test.  With  the  pinhole  the  vision  is  not 
quite  as  good  as  with  the  refraction  correction,  as  it  excludes  a  great 
deal  of  light.  When  using  it  the  card  should  be  very  well  illumined. 
In  testing  the  vision  of  diseased  eyes  which  have  at  the  same  time 
errors  of  refraction  this  method  is  of  utility  as  we  wish  to  know  how 
much  poor  vision  is  due  to  the  disease  and  how  much  to  the  error  of 
refraction. 

Following  the  routine  method  no  matter  whether  the  vision  is 
below  par  or  not,  weak  convex  spherical  lenses  are  placed  in  the 
trial  frame  before  the  patient's  eyes.  If  hyperopia  exists  the  patient 
will  see  just  as  well  with  the  lens  on  as  with  it  off,  or  as  we  say 
vision  is  maintained  with  the  convex  lens.  This  would  not  be 
possible  unless  the  eye  relaxed  some  accommodation  and  allowed 
the  glass  lens  to  take  its  place,  and  the  fact  that  the  eye  was  using 
accommodation  for  distant  objects  proves  the  presence  of  hyperopia. 

The  test  is,  not  does  the  patient  see  better,  but  does  he  maintain 
the  same  vision  with  the  glass.  If  the  error  is  high  he  may  even  see 
better  with  the  lens  on,  as  will  always  happen  if  his  unaided  vision 
is  below  20/20.  The  case  in  hand  is  not  under  the  effect  of  a  cyclo- 
plegic.  Under  a  cycloplegic  the  convex  lens  either  makes  vision 
better  or  worse.  If  the  visual  acuity  is  the  same  in  each  eye  and 
keratometry  shows  little  or  no  astigmatism  one  may  begin  by  plac- 
ing the  same  strength  lens  before  each  eye,  and  then  the  strength 
increased  until  the  strongest  that  allows  the  patient  to  see  as  well 


DETECTION   AND   CORRECTION   OF    ERRORS   OF   REFRACTION.     279 


or  renders  the  \asion  best  is  ascertained.     The  idea  is  to  get  the 

patient  to  relax  all  the  accommodation  possible,  and  thus  to  reveal 

the  greatest  amount  of  error. 

At  times  this  is  accomplished 

better  by  placing  before   the 

eyes  at  first   lenses  that  are 

too  strong  to  see  clearly  with 

and  then  gradually  diminish- 
ing them,  until  the  strongest 

pair  is  ascertained  that  allows 

of  the  best  vision.     A  shade 

should  now  be  placed  before 

one  eye  and  the  lens  before 

the  other  altered   and  made 

stronofer  or  weaker,   if  need 

be  to  make  the  vision  the  best 

possible :   the   strongest  lens 

within  these  limits  of  course  being  selected,  and  so  with  the  other 

eye.  The  lenses  thus  as- 
certained are  to  be  pre- 
scribed, if  the  patient 
shows  no  evidence  of  as- 
tigmatism. The  latter  will 
most  hkely  exist  if  in  de- 
feult  of  any  intra-ocular 
lesion  the  vision  is  still 
below  par  with  the  proper 
spherical  lenses.  The  tests 
for  astigmatism  should  al- 
ways be  applied  however 
as  there  may  be  as  much 
as  1  D.  of  astigmatism 
present  and  the  vision  nor- 
mal.    As  will  be  recalled. 


.S-.;^)(i)|B;,Sj, 

^ 

m. 

~4S    1 

15^ 

^^1. 

^^^■iH^^i 

loll' 

^^5  ^ 

R^ 

^^H 

13 

^1 

28o 


THE    EYE,    ITS    REFRACTION   AND    DISEASES. 


the  astigmatic  eye  can  not  focus  equally  well  in  all  directions  or 
meridians  at  once ;  it  happens  therefore  that  such  an  eye  can  not  see 
lines  drawn  in  different  directions  with  equal  distinctness.  The  line 
that  runs  at  right  angles  to  the  meridian  that  has  the  sharpest  focus- 
ing will  be  seen  the  best.  The  patient  with  the  convex  spherical 
lenses  before  his  eyes,  that  correct  the  hyperopia,  is  then  made  to  look 
at  a  chart  made  after  the  manner  of  either  one  shown  in  the  cuts. 


Green's  Imi'koveo. 


4.     Dr.  Jno.  Green's. 


The  chart  most  commonly  used  is  Dr.  Green's,  style  no.  4.  Num- 
ber I  or  2  is  however  the  most  convenient,  as  the  meridians  are 
marked  every  fifteen  degrees  apart.  The  meridians  upon  the  card 
are  numbered  around  from  the  left  to  the  right  as  the  hands  of  the 
watch  move,  from  o  degrees  at  nine  o'clock,  to  180  degrees  at  three 
o'clock.  Both  ends  of  the  horizontal  line  are  frequently  marked 
180,  as  in  charts  i  and  2.  Besides  the  astigmatic  dials  there  are 
several  other  tests  for  astigmatism,  one  of  the  best  is  Dr.  Pray's 
astigmatic  letters.  As  will  be  seen  by  referring  to  the  figure,  these 
letters  are  made  of  stripes  running  in  a  different  direction  in  each 
letter.  In  using  card  no.  3  the  patient  should  notice  whether  the 
white  sectors  appear  equally  distinct  in  every  direction,  and  if  he 
can  trace  them  equally  well  towards  the  center  in  all  directions.     In 


DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION.  28 1 

using  Dr.  Hill's  card,  the  striped  line  is  rotated  so  as  to  occupy  dif- 
ferent meridians,  the  patient  watching  the  line  as  it  rotates,  and  notic- 
ing whether  the  cross  lines  appear  more  distinct  in  one  direction  of 
the  line  than  in  another.  If  on  card  no.  4  the  cross  lines  are  seen 
the  best,  the  line  on  Hill's  card  will  be  seen  best  when  vertical,  as 
then  in  each  case  the  stripes  are  crosswise.  In  using  Prays  card 
the  individual  notices  if  all  the  letters  are  black  and  distinct  alike. 


^==  ^=5?=    >s^ 

m  u  =r 

ll"llli  ///"ii    'v% 

'liiilii  O  M 

'^  my&  o*"vc 


Fray's  Letters.  Hill's  Card. 

Upon  the  same  principle  there  is  made  a  card  with  a  number  of 
circles  striped  in  different  directions  in  each.  The  cut  below  shows 
a  recent  astigmatic  card.  The  fact  that  all  the  lines  or  letters  look 
alike  is  no  evidence  that  there  is  no  astigmatism  present  in  an 
eye  7iot  under  the  action  of  a  cycloplegic.  Even  if  all  the  lines  do 
appear  alike,  further  attempt  should  be  made  to  render  manifest 
any  latent  astigmatism.  This  is  accomplished  by  Javal's  or  Bull's 
fogging  method.  A  convex  spherical  lens  strong  enough  to  percep- 
tibly blur  the  vision  is  placed  in  the  trial  frame,  in  front  of  the  cor- 
recting lenses.  The  tendency  on  the  part  of  the  eye  is  to  relax  any 
accommodation  that  may  be  in  use,  in  attempt  to  render  the  vision 
better.  (Blurred  retinal  pictures  are  always  a  stimulus  for  the  action 
or  relaxation  of  the  ciliary  muscle,  adjustment  taking  place  until  the 


282 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


best  vision  is  obtained.)  The  fogging  lens  (spherical  lens)  should 
not  be  strong  enough  to  blur  out  of  sight  the  lines  upon  the  astig- 
matic dial.  If  with  this  lens  on,  the  lines  all  look  equally  blurred, 
the  lens  should  be  made  weaker  or  stronger,  and  the  lines  again 
looked  at.  If  they  all  appear  alike  still,  there  is  most  likely  no  astig- 
matism present. 

The  strength  of  the  fogging  lens  should  be  changed  for  it  is  pos- 
sible that  there  may  be  astigmatism  present,  but  which  is  rendered 
mixed  astigmatism  by  the  convex  lens,  being  of  a  strength  that 
brings  the  focus  of  the  least  hyperopic  meridian  now  upon  the  retina 


Fiel 


Fii.. ». 


Verhoeff's  Astigmatic  Dials. 

by  aid  of  the  lens  that  corrects  the  hyperopia  anterior  to  the  retina, 
while  it  brings  the  focus  of  the  most  hyperopic  meridian  behind  the 
retina  forward  to  the  same  extent.  The  amount  of  hyperopia  and 
myopia  being  equal  in  the  mixed  astigmatism  thus  produced  the  size 
3f  the  diffusion  circles  for  all  meridians  of  the  eyeball  will  be  the 
:jame,  and  therefore  all  the  lines  upon  the  astigmatic  cards  appear 
alike.  The  fogging  lens  must  be  greater  than  the  amount  of  astig- 
matism, therefore.  If  all  the  lines  do  not  look  alike  either  with  or 
without  Bull's  method,  there  remains  an  error  of  astigmatism  to  be 
corrected.     It  is  well  to  turn  the  chart  around  especially  when  ex- 


DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION.  283 

amining  children  to  see  if  the  same  meridian  is  always  selected  irre- 
spective of  the  position  of  the  chart,  or  whether  the  patient  simply 
follows  the  same  line  as  it  is  moved  through  different  meridians.  If 
the  latter  is  done,  the  answers  given  can  not  be  relied  upon  and  it  is 
better  to  at  once  instil  a  cycloplegic  and  examine  the  case  objectively. 
Any  existing  astigmatism 
after  the  hyperopia  has 
been  corrected  by  the 
strongest  convex  spheri- 
cal lens,  with  which  dis- 
tant vision  is  maintained, 
or  when  overcorrected  as 
is  done  in  the  fogging  method,  is  converted  into  myopic  astigmatism. 
The  figure  represents  a  compound  hyperopic  astigmatic  eye,  in 
which  the  horizontal  meridian  of  the  cornea  H  is  the  most  hyperopic. 
A  is  the  principal  focal  point  of  the  vertical  meridian,  and  b  that 

of  the  horizontal  meridian.  The 
convex  spherical  lens  L  brings 
both  focal  points  forward,  causing 
the  most  hyperopic  to  be  brought 
upon  the  retina  and  the  least 
hyperopic,  anterior  to  it,  or  per- 
haps both  focal  points  are  brought 
anterior  to  the  retina.  This  myopic  astigmatism  is  corrected  by  a 
concave  cylindrical  lens  with  its  axis  parallel  to  the  meridian  of  the 
eyeball  that  is  not  to  be  influenced,  or  what  is  the  same  thing  at  right 
angles  to  the  line  upon  the  dial  that  is  seen  the  best. 

This  will  be  dealt  with  more  fully  under  the  head  of  correction  of 
astigmatism.  Of  course  the  sphero-cylindrical  combination  must  be 
reduced  to  one  with  like  signs  for  sphere  and  cylinder,  a  plus  sphere 
combined  with  a  plus  cylinder,  for  the  reasons  noted  upon  page  251. 
It  is  impossible  to  ascertain  the  full  amount  of  latent  hyperopia  and 
astigmatism  without  the  use  of  a  cycloplegic.  The  latent  hyperopia 
may  not  give  rise  to  trouble,  but  latent  astigmatism  seldom  fails  to 


284 


THE   EYE.    ITS   REFRACTION   AND    DISEASES. 


annoy,  so  it  is  much  better  if  there  is  any  reason  to  suppose  from  the 
contradictory  evidence  gained  through  subjective  examination  that 
there  is  latent  astigmatism  to  instil  a  cycloplegic  and  examine  the 
case  objectively. 

It  may  happen  that  during  the  subjective  test  the  patient  will 
accept  the  weakest  convex  sphere,  that  is  the  one  that  corrects  the 
least  ametropic  meridian  of  the  eyeball.  Under  these  conditions  a 
concave  cylinder  exaggerates  the  astigmatism,  which  is  made  evident 
by  the  fact  that  all  the  lines  upon  the  astigmatic  chart  look  more 

uniform  without  the  lens 
than  they  do  with  it  on.  A 
convex  cylinder  is  needed 
then  to  correct  the  astigma- 
tism (see  figures). 

Each  of  the  cases  repre- 
sented show  astigmatism 
with  the  rule,  that  is  the 
most  hyperopic  meridian  is 
crosswise.  In  figure  I  the 
lens  L  corrects  the  meridian 
of  the  least  hyperopic,  caus- 
ing the  principal  focus  of  the 
vertical  meridian  to  lie  upon 
the  retina.  The  horizontal  lines  upon  the  astigmatic  card  are  then 
seen  the  best  as  they  are  focused  through  the  vertical  meridian  of 
the  eye.  In  figure  II  the  lens  L  corrects  the  most  hyperopic  meri- 
dian, the  other  principal  meridian,  bringing  the  focus  of  the  cross 
meridian  upon  the  retina,  but  at  the  same  time  carrying  the  focus  of 
the  vertical  meridian  in  front  of  the  retina,  giving  rise  to  a  myopic 
astigmatism.  The  vertical  lines  are  now  seen  the  best  inasmuch  as 
their  focus  lies  upon  the  retina.  In  case  no.  i,  a  convex  cylinder, 
axis  vertical,  corrects  the  astigmatism,  while  in  case  no.  2  a  concave 
cylinder  with  its  axis  at  180,  or  horizontal,  is  needed.  As  a  rule 
then  use  a  convex  cylinder  to  clear  up  vertical  lines  and  a  concave 


DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION.  285 

one  to  clear  up  horizontal  lines.  This  rule  applies  to  astigmatism 
with  the  rule,  the  reverse  being  true  in  astigmatism  against  the  rule, 
that  is,  a  concave  cylinder  for  clearing  cross-lines  and  a  convex  cylin- 
der for  clearing  up  vertical  lines. 

The  cylinders  are  placed  before  the  eye  with  their  axes  at  right 
angles  to  the  lines  upon  the  astigmatic  dial  that  are  seen  the  most 
distinctly.  (The  same  thing  as  placing  the  axis  of  the  cylinder  across 
or  parallel  to  the  nearest  emmetropic  meridian  of  the  eyeball.) 
When  the  accommodation  is  in  abeyance  through  the  use  of  a 
mydriatic,  the  aim  is  to  ascertain  the  lens  that  gives  the  best  vision. 
From  this  lens  or  combination  must  be  deducted  .25  D.  for  the  re- 
turn of  tone  of  the  ciliary  muscle,  and  in  addition  the  amount  of 
accommodation  that  would  be  needed  for  the  distance  at  which  the 
refraction  work  is  done.  The  tone  of  the  ciliary  muscle  is  really  a 
partial  contraction,  which  is  relaxed  by  use  of  the  cycloplegic  and 
regained  after  the  latter  wears  off.  If  there  is  a  weakness  of  the 
internal  recti  muscles,  a  further  deduction  must  be  made  after  the 
manner  described.  The  greater  the  inefficiency  of  the  interni  the 
more  is  to  be  deducted  and  vice  versa. 

The  younger  the  individual  the  greater  the  amount  of  latent  error, 
so  more  hyperopia  has  to  be  deducted  from  the  total  correction  in 
the  young  than  in  those  of  more  advanced  years.  The  only  exact 
way  to  determine  how  much  to  deduct  to  allow  for  the  return  of 
accommodation  is  to  reexamine  the  patient  after  the  effect  of  the 
cycloplegic  has  worn  off.  A  certain  amount  of  experience  in  re- 
fraction work  enables  one  to  tell  how  much  to  deduct  in  the  majority 
of  cases. 

If  the  patient  refuses  convex  spherical  lenses,  that  is  if  the  vision 
is  rendered  worse  by  them,  hyperopia  is  excluded.  Concave  spheri- 
cal lenses  are  then  placed  before  the  eyes  until  the  weakest  lens  is 
found  that  allows  of  the  best  distant  vision.  Both  eyes  may  be 
tested  together,  and  after  the  lenses  are  found  that  give  the  best 
vision  the  lens  before  each  eye  modified  to  suit  it,  being  made  a 
little  stronger  or  weaker  as  the  case  may  be,  or  one  eye  at  a  time 


286 


THE   EYE,    ITS   REFRACTION   AND   DISEASES, 


may  be  tested.  In  myopia  we  select  the  weakest  lens  with  which  the 
patient  can  see  the  best,  as  the  patient  can  see  just  as  well  with  one 
a  little  too  strong  by  using-  his  accommodation.  Under  these  condi- 
tions the  myopia  is  said  to  be  overcorrected  and  the  patient  is  left 
hyperopic,  with  all  the  eye-strain  that  hyperopia  entails.  Whenever 
myopes  are  allowed  to  select  glasses  for  themselves  they  most  always 
select  them  too  strong. 

Figure  lis  a  myopic  eyeball,  A  its  posterior  principal  focus.     By  aid 
of  concave  lens  L,  the  parallel  rays  aa'  are  rendered  divergent  and 

therefore  come  to  a  focus  be- 
hind the  retina,  at  the  point 
A' ,  as  the  lens  is  too  strong, 
but  by  the  aid  of  accommo- 
dation as  is  shown  in  figure  II, 
the  focus  A'  can  be  brought 
forward  to  the  point  R  upon 
the  retina,  and  the  eye  secure 
sharp  distant  vision.  For 
this  reason,  that  accommoda- 
tion can  overcome  a  concave 
lens  that  is  too  strong,  con- 
cave lenses  are  never  placed  before  an  eye  in  the  beginning  of  the 
test  as  the  eye  will  of  course  see  as  well  with  the  glass,  and  by  the 
fact  that  the  letters  are  made  smaller  by  the  concave  lenses,  and 
therefore  blacker,  the  patient  may  think  that  the  lens  has  increased 
his  visual  acuity.  After  the  proper  spherical  lens  has  been  decided 
upon,  one  proceeds  to  test  for  astigmatism.  In  myopia  the  fogging 
method  is  applied  by  placing  before  the  eye  a  concave  spherical  lens 
that  is  too  weak  and  which  therefore  leaves  the  vision  much  blurred. 
Under  these  conditions,  if  the  lens,  before  the  eye  corrects  the  least 
myopic  meridian  of  the  eyeball,  a  concave  cylinder  will  be  needed  in 
addition,  to  correct  the  astigmatism,  applied  at  right  angles  to  the 
Ime  seen  the  best  upon  the  astigmatic  chart,  while  if  the  concave 
sphere  before  the  eye  corrects  the  most  myopic  meridian,  at  the  same 


DETECTION   AND   CORRECTION   OF   ERRORS   OF   REFRACTION.     287 

time  rendering  the  least  myopic,  hyperopic,  a  convex  cylindrical  lens 
will  be  required  to  make  all  the  lines  appear  uniform.  The  resulting 
sphero-cylindrical  combination  must  then  be  reduced  to  one  of  like 
signs.  In  hyperopia  and  myopia  when  the  spherical  lens  before  the 
eye  is  too  strong  a  cylinder  of  opposite  sign  will  be  needed  to  render 
the  astigmatic  dial  uniform.  In  the  higher  degrees  of  hyperopia  and 
myopia  the  vision  is  frequently  below  par  when  the  ametropia  is 
properly  corrected.  After  the  lenses  that  give  the  best  distant  vision 
in  myopia  have  been  selected,  the  near  vision  should  be  tested  with 
them  on,  and  the  strength  of  them  decreased,  if  need  be  to  give  the 
best  near  vision  at  the  proper  reading  distance. 

If  the  myopia  is  of  high  degree  the  patient  cannot  read  with  his 
distant  glasses,  even  after  a  deduction  of  three  diopters  to  allow  for 
accommodation  being  nil,  on  account  of  concave  lenses  diminishing 
the  size  of  the  retinal  images.  In  such  a  case  the  concave  lenses 
must  be  reduced  in  strength  and  the  patient  allowed  to  bring  the 
print  closer  to  the  eyes,  'until  the  best  vision  is  obtained  at  the  great- 
est distance.  If  both  eyes  are  now  being  used,  denoted  by  conver- 
gence for  this  point,  or  by  the  stereoscope,  prisms  should  be  added 
with  bases  towards  the  nose,  so  that  the  eyes  while  regarding  a  close 
point  will  need  no  more  convergence  than  if  they  were  being  used 
for  a  distance  of  33  cm.  Thus,  suppose  the  greatest  distance  at 
which  the  patient  can  read  is  20  cm.  For  that  distance  five  meter- 
angles  of  convergence  are  needed  (see  measurement  of  convergence) 
while  only  three  meter-angles  are  needed  for  a  distance  of  33  cm. 
The  patient  must  therefore  have  supplied  a  prism  of  two  meter- 
angles  before  each  eye. 

It  may  be  found  that  the  myope  cannot  read  comfortably  at  ^j 
cm.  on  account  of  the  convergence  being  weak  with  the  accommoda- 
tion. In  such  a  case  prisms  with  bases  in  are  to  be  used  in  addition 
for  reading.  If  the  myope  has  lost  single  binocular  fixation  for  near 
objects  however  it  is  not  wise  to  try  to  restore  it  for  reasons  already 

stated. 

If  a  cycloplegic  is  used  there  is  not  the  same  danger  of  overcor- 


288  THE   EYE,    ITS    REFRACTION   AND   DISEASES. 

recting  myopia  as  there  is  without  it.  The  fogging  method  is  only 
applied  to  detect  astigmatism  when  the  eyes  are  not  under  the  effect 
of  an  agent  that  paralyzes  the  accommodation  muscle,  and  is  only 
intended  to  render  the.ciliary  muscle  quiet  during  the  test,  and  at  the 
same  time  to  reveal  as  much  latent  error  as  possible. 

Astigmatism. — The  astigmatic  individual  frequendy  shows  a  tend- 
ency to  confuse  curved  letters  more  than  others.  In  astigmatism  one 
eye  should  always  be  tested  at  a  time.  If  the  visual  acuity  is  fair, 
and  positive  spherical  lenses  are  refused,  making  the  vision  worse, 
simple  hyperopic  astigmatism  is  suspected.  The  patient  is  then 
asked  to  look  at  one  of  the  astigmatic  test-cards,  with  the  lines  drawn 
in  different  directions,  and  to  note  whether  all  the  lines  appear  uni- 
form. If  the  accommodation  is  active  they  may,  even  if  there  is  a 
considerable  degree  of  astigmatism  present,  by  the  eye  accommodat- 
ing first  for  one  line  and  then  the  other  in  quick  succession,  giving 
the  retina  a  succession  of  distinct  images.  To  obviate  this  as  much 
as  is  possible  the  patient  should  be  told  to'  view  the  central  white 
space  upon  the  card,  and  then  all  the  lines  will  be  seen  at  the  same 
time  and  an  impression  as  to  their  uniformity  or  not  gotten.  After 
the  patient  has  decided  that  the  lines  appear  the  plainer  in  a  given 
direction,  a  card  with  lines  drawn  in  that  direction  and'  at  right  angles 
thereto  is  placed  before  him.  If  he  views  these  crossed  lines  with  his 
accommodation  in  abeyance,  the  lines  that  run  at  right  angles  to  the 
emmetropic  meridian  of  the  eye  will  be  seen  the  plainer,  but  if  accom- 
modation is  used,  those  that  are  parallel  to  the  emmetropic  meridian 
will  appear  the  plainer.  This  fact  must  ever  be  borne  in  mind,  other- 
wise a  case  of  hyperopic  astigmatism  will  often  be  corrected  for  one 
of  myopic  astigmatism  (see  figures). 

Both  of  these  figures  represent  simple  hyperopic  astigmatism 
with  the  rule.  No.  I  is  represented  as  viewing  crossed  lines, 
with  relaxed  accommodation.  Line  i  is  focused  through  meridian 
I  of  the  eyeball,  and  line  2,  through  meridian  2.  The  horizon- 
tal lines  are  seen  the  better  as  their  focus  is  upon  the  retina. 
No.  II  represents  the  eye  as  looking  at  crossed  lines,  using  accom- 


DETECTION   AND    CORRECTION   OF   ERRORS    OF    REFRACTION.     289 


modation.     The  increased  convexity  of  the  crystalline  lens  brings 
both   foci   forward.     The   vertical   lines   are   now  seen   the   better 
as  their  focus  is  upon  the  retina.     If  the  astig- 
matism is  against  the  rule,  that  is  the  flatter 
curve  of  the  cornea  being  vertical,  the  vertical 
lines  will  be  seen  the  better  when  the  accommo- 
dation is  in  abeyance,  and  vice  versa.     Simple 
hyperopic   astigmatism  is   corrected  by  a  plus 
cylinder  with  its  axis  parallel  to  the  emmetropic 
meridian  of  the  eye,  that  is  perpendicular  to  the 
best  line  seen,  if  the  accommodation  is  relaxed 
and    parallel  to  it  if  accommodation    is    being 
used.     As  most  cases  of  astigmatism  are  those 
with  the  rule,  it  may  be  said  that  usually  a  posi-  ^ 
tive  cylinder,  with  its  axis  vertical  or  at  90  de- 
grees is  needed  to  correct  hyperopic  astigma-    " 
tism. 

A  very  common  error  of  some  opticians  is  to 
correct  the  pseudomyopic  astigmatism  produced 
by  accommodation  as  shown  in  opposite  fig- 
ure as  one  of  true  myopic  astigmatism,  with  a 
concave  cylindrical  lens,  placed  at  right  angles 
to  the  best  seen  line  upon  the  chart.  The 
myopic  cylinder  lengthens  the  myopic  focus  (2), 
and  causes  it  to  lie  upon  the  retina  with  focus 
no.  I.  The  astigmatism  is  corrected  and  now 
all  the  lines  upon  the  astigmatic  dial  look  uni- 
form, but  the  eye  is  left  hyperopic,  using  its 
accommodation  to  focus  distant  objects  as  it 
was  the  action  of  the  ciliary  muscle  that  trans- 
formed the  case  into  one  of  myopic  astigmatism. 
Always  follow  this  rule  :  If  the  eye  is  not  under 
the  effect  of  a  cycloplegic,  no  matter  what  line 
upon  the  card  appears  the  best,  try  first  with  a  plus  cylinder  to  cor- 
19 


290  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

rect  the  astigmatism,  placing  it  before  the  eye  with  its  axis  parallel 
to  the  best  line  seen.  If  the  case  is  one  of  hyperopic  astigmatism 
in  which  accommodation  is  being  used,  it  will  be  relaxed  and  the 
curve  of  the  cylinder  crosswise  before  the  eye  will  shorten  the  cross- 
focusing  of  the  eyeball  and  bring  the  focus  of  the  vertical  lines  upon 
the  retina,  and  all  the  lines  will  appear  uniform,  of  the  same  shade, 
and  at  the  same  time  the  vision  will  be  rendered  better. 

If,  on  the  other  hand,  the  case  is  one  of  simple  hyperopic  astigmatism 
with  relaxed  accommodation  a  plus  cylinder  placed  before  the  eye 
with  its  axis  parallel  to  the  best  line  seen,  will  render  the  horizontal 
focusing  of  the  eye  myopic,  bringing  it  in  front  of  the  retina.  Verti- 
cal and  horizontal  lines  will  be  made  to  appear  alike,  by  the  blurring 
of  the  horizontal  or  previously  better  line,  but  the  visual  acuity  will 
not  be  improved.  Then  the  cylinder  is  to  be  turned  until  the  axis  is 
at  right  angles  to  the  best  line  upon  the  card.  A  plus  spherical  lens 
may  be  accepted  by  the  astigmatic  eye  using  accommodation,  simply 
allowing  the  glass  to  do  what  the  accommodation  did,  that  is,  to 
transform  the  case  into  one  of  pseudo-myopic  astigmatism.  A  con- 
cave cylinder  at  right  angles  to  the  best  line  is  then  needed  to  make 
the  lines  appear  all  alike,  and  to  render  the  vision  normal.  In  cases 
of  simple  hyperopic  astigmatism  the  strength  of  cylin'der  needed  will 
be  found  to  be  equal  to  the  strength  of  the  sphere  already  on,  and 
the  equivalent  lens  will  be  a  plus  cylinder  of  the  same  strength  as  the 
concave,  but  with  its  axis  at  right  angles  to  the  latter,  and  which 
should  be  substituted  for  the  combination  of  plus  sphere  and  concave 
cylinder. 

The  same  method  is  followed  in  simple  hyperopic  astigmatism — if 
the  eye  was  not  accommodating  for  the  lines  upon  the  card,  but  a 
convex  sphere  was  accepted.  When  the  eye  is  not  under  a  cyclo- 
plegic,  it  is  whether  the  eye  sees  as  well  with  a  convex  sphere  as 
with  none  and  not  whether  it  sees  better.  In  ascertainine  the  kind 
of  cylinder  and  inclination  of  axis  needed,  a  +  .50  D.  is  a  convenient 
strength  to  use.  If  all  the  lines  should  look  uniform  to  the  patient 
under  examination  a  convex  sphere  is  placed  before  the  eyes  to  en- 


DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION.  29 1 

courage  the  relaxation  of  accommodation,  fogging  the  lines  upon  the 
astigmatic  card.  Any  existing  astigmatism  is  then  converted  into 
myopic  astigmatism  and  corrected  after  the  manner  of  the  latter.  If 
a  convex  spherical  lens  is  first  accepted,  before  astigmatism  is  cor- 
rected, diminish  its  strength  or  remove  it,  if  the  vision  is  not  20/20  or 
better  with  it,  as  has  been  noted  the  sphere  like  the  accommodation  has 
caused  pseudo-myopic  astigmatism,  which  in  turn  was  transformed  into 
myopia  by  the  application  of  the  convex  cylinder  applied  according 
to  the  rule  when  the  eye  is  not  at  rest,  that  is  parallel  to  the  best 
seen  line.  In  the  higher  degrees  of  simple  hyperopic  astigmatism  the 
axis  of  the  correcting  cylinder  is  always  placed  before  the  eyes  at 
right  angles  to  the  best  seen  line  whether  the  eyes  are  under  a  cyclo- 
plegic  or  not,  as  the  accommodation  does  not  endeavor  as  in  the  low 
degrees  of  error  to  render  it  latent.  If  the  astigmatism  is  over 
several  diopters  the  ciliary  muscle  never  converts  the  hyperopic  case 
into  a  myopic  one. 

Now  and  again  the  patient  will  not  accept  the  cylindrical  lens  that 
corrected  the  astigmatism  when  the  eyes  were  under  the  effect  of  a 
cycloplegic,  when  the  latter  wears  away.  The  brain  seems  to  have 
become  accustomed  to  interpret  distorted  images  from  early  child- 
hood, and  does  not  immediately  appreciate  the  benefit  of  perfectly 
formed  retinal  pictures.  For  the  same  reason  in  some  a  cylinder 
fails  to  improve  the  vision  to  any  marked  extent  even  when  the  error 
is  high.  The  rule  is  thought  to  correct  all  the  astigmatism.  Such 
cases  as  those  just  mentioned  will  finally  accept  the  proper  strength 
cylinder,  if  the  glass  is  worn  while  the  effects  of  the  cycloplegic  is 
wearing  off,  or  if  the  eye  be  led  up  to  the  proper  strength,  by  begin- 
ning with  weaker  cylinders  of  the  same  kind  and  gradually  increas- 
ing their  strength  at  intervals  of  several  days  or  weeks  as  the  case 
may  be,  until  the  proper  one  is  worn. 

There  are  infrequent  cases  that  appear  to  be  more  comfortable 
without  the  astigmatic  correction.  The  majority  of  these  however 
are  cases  in  which  the  proper  correction  has  not  been  obtained  and 
as  a  rule  cases  that  have  only  been  examined  subjectively  without 


292  THE   EYE.    ITS   REFRACTION   AND   DISEASES. 

the  use  of  any  agent  to  relax  the  ciliary  muscle.  There  are  though 
a  few  cases  of  compound  hyperopic  astigmatism,  cases  that  are  more 
comfortable  without  the  correcting  cylinders,  wearing  simply  spheres 
to  correct  their  hyperopia.  There  is  no  way  to  tell  this  beforehand. 
Correct  the  full  error  of  astigmatism  and  look  after  muscular  anom- 
alies and  then  if  the  eyes  are  not  comfortable  the  cylinders  should  be 
reduced  or  omitted,  especially  if  they  do  not  in  a  marked  degree  im- 
prove the  visual  acuity.  To  be  certain  that  one  has  ascertained  the 
meridians  of  the  least  and  the  greatest  refraction  of  the  eye  without 
the  use  of  a  cycloplegic  is  impossible ;  the  lines  that  have  their  focus 
upon  the  retina  are  seen  the  best,  and  these  may  be  in  the  meridians 
corresponding  to  the  principal  meridians  of  the  eye  or  to  some  other, 
according  to  the  amount  of  accommodation  being  used  during  the 
testing.  However  this  makes  little  difference  in  most  cases.  To  be 
reasonably  certain  that  the  patient  is  not  guessing  or  that  the  accom- 
modation is  not  interfering  much  with  the  test,  it  is  well  to  have  the 
patient  pick  out  the  most  blurred  as  well  as  the  best  seen  lines 
upon  the  card,  as  the  two  must  always  be  at  right  angles  to  each 
other,  unless  there  is  present  irregular  astigmatism,  and  this  would 
be  noted  by  pathological  changes  in  the  cornea  scars  or  change  in  its 
shape,  which  could  be  detected  by  oblique  illuminati6n,  by  incipient 
cataract  or  obliquity  of  the  crystalline  lens,  detected  by  the  ophthal- 
moscope. 

In  the  practical  application  of  the  test  for  astigmatism,  one  begins 
with  a  weak  plus  cylinder,  placed  before  the  eye  according  to  the 
rules  laid  down,  and  if  the  lines  are  rendered  more  alike  by  it,  it  is 
of  the  right  sign  and  inclination ;  successively  stronger  and  stronger 
cylinders  are  then  placed  before  the  eye  until  the  one  is  found  that 
makes  all  the  lines  appear  exactly  alike.  If  one  is  chosen  that 
causes  the  previously  blurred  line  to  appear  the  better,  it  is  too 
strong  and  is  said  to  have  overcorrected  the  astigmatism.  The  next 
weaker  cylinder  is  then  chosen.  If  two  successive  strengths  are 
found,  the  one  under  and  the  other  overcorrecting  the  astigmatism, 
the  former  is  to  be  chosen.     In  simple  hyperopic  or  myopic  astig- 


DETECTION   AND   CORRECTION   OF   ERRORS  OF   REFRACTION.     293 


matism  the  formerly  blurred  line  is  never  made  the  better  by  a 
cylindrical  lens  that  overcorrects  the  astigmatism.  The  lines  at  right 
angles  to  one  another  become  more  and  more  alike  until  the  cor- 
recting cylinder  is  ap- 
plied, when  they  are  ex-  so" 
actly  alike.  If  a  cylin- 
der too  strong  is  now 
put  before  the  eye  the 
lines  that  appeared  the 
better  without  any  lens 
again  begin  to  be  seen 
the  plainer.  It  is  there- 
fore necessary  to  in- 
crease the  strength  of 
the  cylinder  gradually 
in  correcting  astigma- 
tism, or  otherwise  one 
may  overcorrect  the 
case,  and  from  the  ap- 
pearances of  the  lines 
suppose  that  the  proper 
strength  cylinder  has 
not  yet  been  arrived  at. 
The  fact  that  a  cylin- 
drical lens  reverses  the 
lines,  that  is  causes  the 
opposite  lines  to  appear 
the  better,  is  proof  that 
the  astigmatism  is  com- 
pound, that  is,  that  the 
hyperopia  or  myopia 
has  not  been  corrected. 
Such  cases  should  have  a  cycloplegic  instilled. 

In  figure  I,  light  rays  i,  2  from  cross  lines  pass  into  the  eyeball 


294  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

through  the  vertical  meridian,  and  are  focused  upon  the  retina  ;  ergo : 
they  are  seen  plainer  than  the  vertical  lines,  whose  focus  is  behind  the 
retina  at  x. 

Figure  II  is  a  case  of  compound  hyperopic  astigmatism.  The 
focus  through  the  vertical  meridian  of  the  eyeball  is  nearest  accurate, 
therefore  cross-lines  are  seen  the  clearer  by  the  eye. 

Figure  III  represents  simple  hyperopic  astigmatism  overcorrected 
by  a  plus  cylinder.  The  cylinder  brings  the  focus  through  the  cross 
meridian  anterior  to  the  retina.  The  horizontal  lines  still  have  their 
focus  upon  the  retina  and  are  therefore  seen  the  better,  as  in  case 
no.  I,  where  the  astigmatism  was  uncorrected. 

Figure  IV.  Compound  hyperopic  astigmatism  overcorrected  by  a 
plus  cylinder.  The  focus  b  through  the  vertical  meridian  is  not 
altered,  but  the  cylinder  has  brought  the  focus  a  through  the  cross 
meridian  of  the  eyeball  upon  the  retina,  and  therefore  the  vertical 
lines  are  seen  the  better.  The  astigmatism  was  corrected  when  a 
was  brought  to  b,  but  is  now  overcorrected. 

There  are  some  that  are  unable  to  discern  any  difference  in  the 
distinctness  of  the  lines  upon  the  astigmatic  dial  even  when  a  great 
deal  of  objective  astigmatism  is  present.  Their  eyes  have  always 
been  accustomed  to  see  things  in  a  distorted  manner  and  any  dif- 
ference in  the  distinctness  of  the  lines  upon  the  dial  is  considered 
normal.  One  can  often  bring  to  the  attention  of  such  a  case  the  fact 
that  all  the  lines  do  not  look  alike  by  placing  a  strong  plus  cylindri- 
cal lens  before  the  eye.  The  lines  that  run  at  right  angles  to  the 
cylinder  are  seen  the  best,  the  axis  of  the  cylinder  is  then  changed. 
After  the  difference  in  the  distinctness  of  the  lines  has  been  noted 
several  times  the  cylinder  is  removed,  when  the  astigmatic  patient 
will  still  notice  a  difference  in  the  lines,  caused  by  his  error  of  refrac- 
tion. Now  and  then  one  will  say  that  the  lines  on  the  astigmatic 
dial  are  seen  better  on  one  side  of  the  center  of  the  card  than  on  the 
other.  This  is  mostly  imaginative,  but  in  a  few  cases  is  caused  by 
astigmatism  by  incidence,  that  is  obliquity  of  the  crystalline  lens  of 
the  eye,  or  by  an  oblique  position  of  the  screen  or  retina  as  in  eyes 


DETECTION    AND    CORRECTION    OF    ERRORS   OF    REFRACTION.      295 

with  posterior  staphylomata.  This  may  be  corrected  by  tilting  the 
lenses  before  the  eye.  Astigmatism  that  can  not  be  ascertained  by 
the  usual  methods  can  be  revealed  by  placing  a  weak  convex  cylin- 
der in  the  trial  frame  and  rotating  it  through  1 80  degrees.  If  the 
vision  is  found  to  be  better  in  one  position  of  the  cylinder  than  in 
another,  astigmatism  exists.  In  order  that  the  patient  may  notice 
whether  he  sees  better  in  certain  positions  of  the  cylinder,  he  should 
put  his  attention  upon  several  letters  only  in  the  lowest  line  upon  the 
test-card  that  can  be  read.  The  cylinder  should  be  rotated  through 
1 80  degrees  several  times  to  make  sure  that  the  patient  actually  does 
see  better  when  the  axis  of  the  cylinder  has  a  certain  inclination  or 
position.  Folks  over  fifty  frequently  have  astigmatism  against  the 
rule,  which  is  only  discoverable  by  the  increase  of  visual  acuity 
gained  by  placing  a  plus  cylinder  at  180°  or  minus  cylinder  at  90° 
before  the  eye. 

If  a  positive  cylinder  seems  to  blur  the  vision,  whatever  the  direc- 
tion its  axis  occupies,  then  a  minus  cylinder  is  placed  before  the  eye 
and  rotated  in  the  same  manner.  A  .25  D.  C.  is  the  most  conve- 
nient one  to  use  for  this  purpose.  If  a  plus  or  minus  .25  D.  C.  ren- 
ders the  vision  better,  with  the  axis  in  a  certain  position,  then  a  .50 
D.  C.  is  substituted,  and  so  on.  The  cylinder  that  allows  of  the  best 
vision  is  the  one  chosen  as  the  measure  of  the  error.  After  plus 
cylinders  have  been  tried  and  found  to  make  the  lines  upon  the 
astigmatic  dial  more  unlike  or  rendering  them  alike,  spoil  the  visual 
acuity,  the  case  is  considered  to  be  one  of  myopic  astigmatism.  If 
plus  cylinders  make  the  lines  more  unlike,  a  minus  cylinder  is  placed 
in  the  frame,  always  with  its  axis  at  right  angles  to  the  best  seen 
line,  whether  the  eye  is  under  a  cycloplegic  or  not,  and  the  proper 
strength  selected  to  render  the  lines  uniform.  If  the  eye  is  not  under 
a  mydriatic,  there  is  no  way  to  tell,  save  by  trial,  whether  the  case  is 
hyperopia  or  myopia  ;  but  supposing  it  to  be  the  former  and  using 
accommodation  a  plus  cylinder  is  placed  before  the  eye  with  its  axis 
parallel  to  the  best  seen  line.  If  all  the  lines  are  made  alike,  but  the 
vision  is  still  below  par,  then  a  minus  sphere  is  placed  in  front  of  the 


296  THE   EYE.    ITS   REFRACTION   AND    DISEASES. 

cylindrical  lens,  the  weakest  being  chosen  that  allows  of  the  best 
vision.  In  simple  myopic  astigmatism  plus  spheres  will  be  promptly 
refused  as  making  the  vision  worse,  as  they  convert  the  case  into  one 
of  compound  myopic  astigmatism,  by  bringing  the  focal  line  that  is 
upon  the  retina  anterior  to  it.  When  all  the  lines  upon  the  astig- 
matic card  are  seen  more  unHke  or  alike  but  less  distinctly  with  a 
plus  cylinder,  there  is  myopic  astigmatism  present.  In  hyperopic  as- 
tigmatism the  lines  that  are  seen  best  upon  the  astigmatic  chart  with 
the  fogging  glass  on  are  at  right  angles  to  those  that  are  seen  the 
best  without  the  lens,  while  in  myopic  astigmatism  the  same  lines 
appear  the  best  with  and  without  the  fogging  lens. 

Mixed  Astigmatism  is  made  evident  by  the  fact  that  neither  plus 
nor  minus  spheres  improve  the  vision  to  any  extent,  although  the 
pinhole  test  shows  that  the  poor  vision  is  due  to  ametropia,  by  in- 
creasing the  visual  acuity.  Plus  spheres  correct  the  meridian  of 
hyperopia  and  exaggerate  the  meridian  of  myopia,  and  minus  spheres 
correct  the  meridian  of  myopia  and  exaggerate  the  meridian  of 
hyperopia.  If  the  hyperopia  and  the  myopia  are  equal  in  amount  in 
the  principal  meridians  all  the  lines  upon  the  astigmatic  dial  are  seen 
alike,  as  the  diffusion  circles  in  different  meridians  will  be  of  equal 
size.  The  lines  will  however  appear  unequally  distinct,  when  a  con- 
vex or  a  concave  spherical  lens  is  placed  before  the  eye.  The  sphere 
lessens  the  ametropia  in  one  principal  meridian  and  increases  it  in 
the  other. 

If  there  is  a  convex  sphere  on,  the  lines  that  are  seen  the  best  are 
seen  through  the  meridian  of  hyperopia  and  vice  versa.  After  the 
best  seen  line  has  been  chosen  with  the  sphere  on,  say  it  is  a  i  D., 
the  card  with  two  sets  of  lines,  drawn  at  right  angles  to  each  other, 
is  placed  before  the  patient  so  that  one  of  the  sets  of  lines  occupies 
the  meridian  of  the  best  vision.  The  lens  in  front  of  the  eye  is  now 
made  weaker  or  stronger,  until  the  one  is  found  with  which  the  lines 
in  that  meridian  are  seen  the  best,  care  being  taken  to  choose  the 
weakest  concave  or  the  strongest  convex,  as  the  case  may  be.  The 
attention  is  now  placed  upon  the  lines  at  right  angles  to  these,  or  a 


DETECTION   AND    CORRECTION    OF    ERRORS   OF    REFRACTION.      297 

card  upon  which  is  a  single  set  of  Hnes  may  be  used  and  the  Hnes 
made  now  to  occupy  the  opposite  direction.  The  lens  (sphere)  that 
renders  the  lines  best  in  this  position  is  now  ascertained.  If  one 
meridian  needs  a  plus,  the  other  needs  a  minus  and  vice  versa. 
Suppose  for  an  example,  that  when  a  convex  spherical  lens  is  placed 
before  the  eye  that  the  lines  that  occupy  the  meridian  of  60  degrees, 
that  is  those  that  run  between  XI  2S\6.  Kupon  the  dial,  are  seen  the 
best  of  all.  The  meridian  of  the  eye  at  right  angles  to  that,  that  is 
1 50  degrees,  is  the  meridian  of  hyperopia  if  the  eye  is  not  under  a 
cycloplegic,  or  the  meridian  of  least  ametropia  if  the  eye  is  under  a 
cycloplegic.  Lines  are  then  placed  so  that  they  occupy  meridian  of 
60  degrees,  and  the  strongest  convex  sphere  with  which  they  are  seen 
the  best  selected.  Say  it  is  plus  3  D.  S.  Then  the  card  is  turned 
so  that  the  lines  occupy  the  meridian  between  //  and  VIII,  that  is 
1 50  degrees.  Say  that  a  minus  3  D.  S.  now  renders  them  most  dis- 
tinct. The  astigmatism  is  equal  to  the  difference  in  the  strength  of 
the  two  lenses,  or  6  D.,  and  the  correction  is  the  following : 


or 


-  3  D.  S.  O  +  6  D.  Cyl.  ac.  60° 
+  3  D.  S.O-6  D.  Cyl.  ac.  150°. 


The  astigmatism  is  known  to  be  of  the  mixed  variety  from  the  fact 
that  the  sphere  and  cylinder  in  the  combination  are  of  unlike  signs, 
and  the  cylinder  of  greater  strength  than  the  sphere.  The  axis  of 
the  combined  cylinder  in  each  case  is  placed  in  the  meridian  that  is 
corrected  by  the  sphere,  and  the  strength  of  the  cylinder  combined 
with  the  sphere  is  equal  to  the  sum  of  the  refraction  in  diopters  of 
the  two  principal  meridians  of  the  eye. 

If  there  is  a  difference  in  the  lines  noticed  on  first  looking  at  the 
astigmatic  card,  the  examiner  selects  a  weak  positive  spherical  lens, 
and  placing  it  before  the  eye  under  test  asks  the  patient  if  the  lines 
seen  best  without  it  on  are  made  better  with  it  or  if  they  are  at  least 
just  as  good.     If  the  lines  are  seen  just  as  well  with  the  convex 


298  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

sphere  it  argues  that  the  meridian  at  right  angles  to  these  Hnes  is 
hyperopia ;  the  examiner  then  proceeds  as  in  the  former  case.  It  is 
in  this  kind  of  an  error  (mixed  astigmatism)  that  a  cycloplegic  is 
most  needed  to  obtain  accurate  results.  Accommodation  causes  the 
hyperopia  to  be  lessened  and  the  myopia  to  be  increased  to  the  same 
degree,  not  altering  therefore  the  amount  of  the  astigmatism,  but 
leads  one  astray  in  the  estimation  of  the  amount  of  ametropia  in  each 
principal  meridian,  as  accommodation  may  be  used  while  refracting 
one  principal  meridian  and  in  abeyance  while  refracting  the  other. 
After  the  effect  of  the  cycloplegic  has  worn  away  it  will  be  found  that 
the  eye  requires  an  equal  decrease  in  the  strength  of  the  plus  lens 
and  increase  in  the  concave  to  give  it  the  best  vision,  and  to  render 
thq  lines  upon  the  astigmatic  dial  uniform. 

The  same  rules  that  govern  the  amount  to  be  deducted  in  hyper- 
opia apply  whenever  the  hyperopia  is  in  excess  of  the  myopia  and 
the  correction  is  the  same  as  in  myopia  whenever  the  myopia  is  in 
excess  of  the  hyperopia.  To  allow  for  the  return  of  accommodation 
in  mixed  astigmatism,  if  the  combined  sphere  is  positive,  one  simply 
deducts  the  required  amount  from  it,  which  of  course  increases  the 
relative  refraction  of  the  combined  cylinder,  while  if  the  combined 
sphere  has  a  minus  sign,  the  sphere  is  made  stronger,/ which  lessens 
the  refraction  of  the  combined  cylinder. 

In  the  foregoing  pages  it  was  advised  to  ascertain  the  spherical 
correction  first  and  then  to  test  for  astigmatism.  At  times,  however, 
especially  in  mixed  astigmatism  and  compound  astigmatism  of  higher 
degrees,  one  can  do  better  by  correcting  the  astigmatism  first  and 
then  adding  the  proper  sphere.  By  retinoscopy  beforehand  the  sort 
of  astigmatism  is  discovered  and  if  of  the  mixed  variety  the  direc- 
tion of  the  meridians  of  hyperopia  and  myopia  located,  a  cylindrical 
lens  of  the  strength  indicated  by  keratometry  is  then  placed  in  the 
trial  frame  and  modified  until  the  lines  upon  the  astigmatic  dial  are 
rendered  uniform  or  vision  made  best,  then  spheres  are  added  and 
vision  tested.  Each  time  the  sphere  is  changed  the  strength  of  the 
cylinder  and  the  inclination  of  its  axis  is  altered  until  the  best  vision 


DETECTION  AND  CORRECTION  OF  ERRORS  OF  REFRACTION.   299 

is  obtained.  Sometimes  the  following  plan  works  well :  A  sphere 
may  be  dropped  into  the  trial  frame  and  then  the  cylinder  of  ap- 
proximate strength  added.  The  strength  of  the  sphere  and  then 
that  of  the  cylinder  is  changed  until  the  vision  is  rendered  best.  The 
visual  acuity  test  in  astigmatism  should  always  take  precedence  over 
the  other  tests,  for  it  often  happens  that  the  vision  is  not  as  good 
with  the  cylinder  that  makes  all  the  lines  in  the  astigmatic  dial  uni- 
form as  with  one  weaker  or  stronger. 

The  stenopaic  slit  is  at  times  useful  in  the  estimation  of  astigmatic 
errors  of  refraction,  and  especially  so  in  mixed  astigmatism.  A  few 
facts  about  the  stenopaic  slit  in  general,  as  proven  by  photography. 
The  emmetrope  sees  lines  drawn  in  different  directions  perfectly 
uniform,  with  the  stenopaic  slit  before  his  eye,  and  his  vision  is 
practically  the  same  as  without  it,  the  only  difference  being  that  the 
slit  emits  less  light,  and  for  that  reason,  the  vision  may  be  slightly 
impaired  by  it.  If  a  camera  is  put  in  accurate  focus  for  an  astigmatic 
dial,  and  then  a  stenopaic  slit  placed  before  the  objective,  and  a  pic- 
ture taken  of  the  lines  it  will  be  seen  that  all  are  equally  well-defined, 
no  matter  what  the  direction  of  the  slit.  If  the  camera  be  put  out  of 
focus  now  and  a  negative  made  of  the  lines,  those  that  occupied  the 
meridian  upon  the  card  parallel  to  the  slit  are  seen  to  be  in  best 
focus.  The  ametrope  therefore  with  the  stenopaic  slit  sees  the  lines 
parallel  to  the  slit  the  best,  because  the  areas  of  diffusion  upon  the 
retina  are  in  vertical  lines  (when  the  slit  is  vertical  before  the  eye), 
and  these  vertical  diffusion  areas  overlapping  build  up  a  well-defined 
vertical  line  upon  the  retina,  while  the  cross  lines  are  seen  much 
blurred,  because  their  image  upon  the  retina  is  a  broad  blurred  line, 
formed  by  the  apposition  of  the  vertical  diffusion  areas.  Each  point 
in  the  horizontal  lines  is  focused  as  a  vertical  line.  It  follows  that 
an  astigmatic  eye  will  see  best  and  all  the  lines  most  alike  when  the 
stenopaic  slit  occupies  the  meridian  of  least  ametropia.  The  manner 
of  using  the  stenopaic  slit  is  as  follows  :  Place  the  disc  with  slit  in  the 
trial  frame  before  the  eye,  and  slowly  rotate  it  through  180  degrees 
while  the  patient  puts  his  attention  upon  a  certain  line  of  test-type, 


300  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

and  notices  whether  he  sees  better  in  any  particular  position  of  the 
slit  before  the  eye.  If  so  astigmatism  exists  and  the  direction  of  the 
slit  when  the  vision  is  the  best  marks  the  meridian  of  the  least 
ametropia,  the  other  principal  meridian  being  at  right  angles  to  it. 

If  in  the  preferred  position  the  vision  is  20/20  or  better,  and  a 
convex  sphere  is  refused,  or  if  the  eye  is  under  atropine,  there  is 
emmetropia  in  that  meridian.  The  disc  is  now  rotated  so  that  the 
slit  will  occupy  a  position  at  right  angles  to  the  former  one,  and  the 
vision  ascertained.  If  the  vision  is  less  acute  than  before  there 
exists  astigmatism.  A  concave  or  convex  spherical  lens  is  now 
sought  that  will  render  the  vision  normal  in  this  meridian.  The  dif- 
ference in  the  strengths  of  the  two  lenses  needed  to  make  the  vision 
normal  in  the  two  meridians  is  the  measure  of  the  amount  of  the 
astigmatism.  If  in  one  meridian  the  vision  is  normal  and  positive 
spherical  lenses  are  refused,  the  astigmatism  is  of  the  simple  variety, 
while  in  compound  astigmatism  the  vision  will  be  below  par  in  all 
directions  of  the  slit,  better  in  some  however  than  in  others,  and  im- 
proved by  concave  or  convex  spherical  lenses  as  the  case  may  be 
compound  myopic  or  compound  hyperopic  astigmatism.  Mixed  astig- 
matism is  evidenced  by  the  fact  that  a  concave  lens  is  needed  in  one 
meridian  and  a  convex  one  in  the  meridian  at  right  angles  thereto  to 
render  the  vision  perfect. 

In  all  cases  of  astigmatism  of  whatever  variety  after  the  correction 
has  been  applied  according  to  the  rules  laid  down,  it  is  well  to  alter 
the  strength  of  the  sphere,  then  that  of  the  cylinder,  to  see  whether 
the  vision  can  be  made  still  better,  especially  if  one  has  failed  to 
bring  it  to  normal  by  aid  of  the  glasses.  The  cylinder  should  be 
made  a  little  stronger  then  a  litde  weaker  to  see  if  the  vision  is  im- 
proved, by  holding  in  front  of  it  a  weak  cylinder  of  opposite  sign, 
then  one  of  the  same  sign,  the  axis  of  each  being  held  parallel  to  the 
axis  of  the  combined  cylinder  before  the  eye.  Then  the  strength  of 
the  sphere  is  tested  by  holding  in  front  of  the  combination  before 
the  eye  a  weak  convex  and  then  a  weak  concave  spherical  lens.  To 
alter  the  strength  of  the  sphere  and  of  the  cylinder  in  the  correction 


DETECTION   AND    CORRECTION   OF    ERRORS   OF    REFRACTION.      301 

at  the  same  time  is  often  desirable.  This  is  best  done  with  crossed 
trial  cylinders.  These  are  two  cylinders  of  equal  strength  but  of 
opposite  sign  ground  on  one  glass  with  their  axes  at  right  angles  to 
each  other.  The  most  convenient  strengths  are  made  of  .25  D. 
Cyls.  and  of  .50  D.  Cyls.     These  combinations  are  denoted  thus  : 

+  .25  D.  C  I-.25  D.  C.     and    +.50  D.  C.  I-.50  D.  C. 

and  are  equivalent  to 

+  .25  D.  S.  O  — .50  D.  C.     and     +.50  D.  S.  O— i.oo  D.  C. 

The  most  convenient  way  to  have  the  crossed  cylinders  is  mounted 
upon  long  handles  so  that  they  can  be  put  on  and  off  without  the 
hand  obscuring  the  vision.  The  crossed  cylinder  is  placed  before 
the  eye  with  one  of  its  axes  parallel  to  that  of  the  sphero-cylindrical 
combination,  and  vision  noted  and  then  turned  so  as  to  cause  the 
opposite  axis  to  occupy  the  same  position.  If  the  vision  is  made 
better  in  either  direction  of  the  crossed  cylinder  a  change  is  made  in 
the  correction  before  the  eye  accordingly,  the  sphere  in  the  combina- 
tion being  changed  to  the  same  extent  as  the  cylinder.  If  the  one 
is  made  stronger  the  other  is  made  weaker  or  vice  versa.  Thus : 
Suppose  that  before  the  eye  there  is  the  following  combination : 

+  2  D.  S.  O  +  ,50  D.  C.  Ax.  90°,  and  the  patient  saw  better  when 
the  .50  D.  crossed  cylinder  was  placed  before  the  above  combina- 
tion, with  the  axis  of  the  concave  cylinder  parallel  to  that  of  the 
cylinder  in  the  sphero-cylindrical  combination.  The  lens  needed 
then  is : 

(i)  +  2  D.  S.  0  +  .50  D.  C.  Ax.  180°.  If  the  vision  is  improved 
by  rotating  the  crossed  cylinder,  until  the  axis  of  the  positive  cylinder 
is  parallel  to  that  of  the  combined  cylinder,  then  the  glass  needed  is: 

(2)  +  1.50  D.  S.  O  +  1.50  D.  C.  Ax.  90°,  and  so  on. 

Each  time  that  the  sphere  or  the  cylinder  before  the  eye  is 
changed,  the  cylinder  should  be  rotated  a  little  this  way  or  that  to 


302 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


Sphero-cylindrical  Combination. 

0) 

-t-.50  D.  C,= 


+ 

(+2D.  S.C  +  -50 
D.  C.  Ax.  90°) 


ascertain  in  what  position  of  its  axis  the  vision  is  the  best,  that  is  if 
the  eyes  are  not  under  a  cycloplegic  —  for  without  it,  the  principal 
meridians  vary  according  to  the  amount  of  accommodation  used  — 
depending  to  a  certain  extent  upon  the  strength  of  the  plus  S.  before 
the  eye. 

In  high  degrees  of  astigmatism   there  is  often  present  what  the 

author  chooses  to  denominate 
meridional  amblyopia,  that  is 
a  deficient  vision  or  anaesthesia 
of  the  retina  corresponding  to 
the  meridian  of  greatest  ame- 
tropia. In  consequence  it  is 
impossible  to  get  the  eye  to 
see  lines  at  right  angles  to  this 
meridian  with  any  degree  of 
distinctness,  notwithstanding 
the  fact  that  the  astigmatism 
may  be  properly  corrected. 
Such  cases  should  be  corrected 
objectively  and  the  weakest 
cylinder  with  which  the  vision 
is  best  worn. 

Correction  of  Presbyopia.  — 
The  convex  spherical  lens  that 
enables  the  presbyope  to  read 
with    comfort    would    be    too 
strong  for  him  to  work  with  at 
arm's  length,  if  he  was  a  cabi- 
net maker,  and  vice  versa.     In 
prescribing  for  the  presbyope 
one  should  always  ascertain  at 
what  distance  he  wishes  to  use  his  eyes  and  the  glasses  given  accord- 
ingly.    If  we  know  how  much  accommodation  the  patient  has  and 
how  much  he  needs  for  a  given  distance  it  is  not  difficult  to  ascertain 


—.50  D. 


+2.50  D. 


Place  III  upon  II  with 
axis  of  —  cylinder  at 
90°  and  the  resulting 
refraction 


4-2  D 


+  2C-(--5oAx.  180°. 


If  III  is  turned,  so  that  axis  of  -f  cylinder  lies  ver- 
tically, we  have : 


=+1.50  D.S.C+I-50  O.C.AX.go" 


DETECTION    AND    CORRECTION    OF    ERRORS    OF    REFRACTION.      303 

what  he  lacks,  the  amount  to  be  supplied  by  spectacles.  The 
amount  of  accommodation  needed  by  the  emmetrope,  for  any  given 
distance,  is  ascertained  by  dividing  the  distance  expressed  in  centi- 
meters, into  100  centimeters,  or  one  diopter.  This  gives  the  number 
of  diopters  of  accommodation  in  use  for  that  distance,  as  explained 
upon  a  previous  page. 

If  working  in  the  inch  system,  the  distance  in  inches  is  expressed 
in  a  fraction  with  one  as  the  numerator.  Thus  :  How  much  accom- 
modation is  used  when  reading  at  a  distance  of  fifty  centimeters  and 
at  twenty  inches?  Ans.  100/50  =  2  D.  accommodation;  1/20  ac- 
commodation. Any  refraction  error  should  always  be  corrected 
before  the  eyes  are  tested  for  the  presence  of  presbyopia.  The 
presbyopic  correction  is  added  to  the  distant  correction  for  the  near- 
seeing  glasses.  An  emmetropic  bookkeeper  needs  glasses  for  near 
work.  He  is  fifty  years  old.  He  wishes  to  use  his  glasses  at  50 
cm.  distance,  at  his  desk.  Of  late  print  has  been  blurred  at  that 
distance.  The  nearest  point  at  which  he  can  read  with  comfort  is  at 
I  m,,  and  at  that  distance  he  reads  the  type  that  is  designed  to  be 
read  at  that  distance.  (This  shows  that  he  is  emmetropic.)  What 
glasses  does  this  patient  need  ?  How  much  accommodation  does  he 
require  for  the  distance  at  which  he  works  ?  100/50=  2  D.  accom- 
modation needed.  How  much  accommodation  has  he  left  ?  100/ 100 
=  I  D.  accommodation  left.  2  —  1  =  1  D.  accommodation  lost,  and 
needed  to  be  supplied  by  lenses. 

We  would  give  this  patient  a  1.25  D.  S.  lens,  inasmuch  as  a  i 
D.  S.  allows  him  to  read  at  50  cm.  distance  only  when  he  is  using 
all  his  available  accommodation,  and  under  these  conditions  he  would 
soon  tire,  as  all  of  his  accommodative  strength  is  being  put  forth  at 
each  moment.  A  little  stronger  lens  allows  him  to  hold  a  little  ac- 
commodation in  reserve,  and  as  the  ciliary  muscle  is  not  constantly 
exerted  to  its  utmost  the  eyes  do  not  so  soon  tire.  A  patient  may 
come  complaining  that  his  eyes  soon  become  tired  when  using  them 
for  near  things.  He  reads  all  day  long.  The  proper  reading  dis- 
tance is  at  2)3  centimeters,  and  at  that  distance  3  D.  accommoda- 


304 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


tion  are  needed.  The  patient's  near-point  of  accommodation  is  33 
cm.  which  is  only  attained  however  by  straining  the  accommodation, 
as  is  proven  by  the  fact  that  the  patient  can  not  read  a  bit  closer 
than  2,3  cm.  Presbyopia  has  been  troubling  him  since  his  near  point 
has  receded  beyond  22  cm.  (Bonder's  presbyopic  point).  What 
glasses  does  this  man  need  to  make  him  comfortable  ?  The  amount 
of  accommodation  used  for  22  cm.  distance  is  a  trifle  less  than  4.50 
D.  The  patient's  near  point  lies  at  2,3  cm.  representing  3  D.  accom- 
modation. The  patient  has  therefore  lost  since  presbyopia  began 
1.50  D.  accommodation,  which  must  be  supplied  by  convex  spherical 
lenses  in  spectacles.  Presbyopia  then  equals  4.50—  i//,  in  which/ 
=  near  point  of  accommodation  expressed  in  the  metric  system.  If 
the  eyes  have  been  under  the  effect  of  a  mydriatic  for  the  estimation 
of  the  refraction  error,  one  must  wait  until  the  accommodation  has 
fully  returned  before  attempting  to  estimate  the  degree  of  presbyopia. 
It  is  a  bad  policy  to  follow  a  table  and  to  correct  the  presbyopia  ac- 
cording to  the  age  of  the  patient,  for  then  paresis  of  accommodation 
will  certainly  be  overlooked  if  it  exists,  and  not  a  few  people  are  less 
presbyopic  than  their  age  would  indicate. 


Influence  of  Age  on  Accommodation  According  to  Donders. 

Deficiency  of  Refraction  for  25  cm. 

Ages. 

Ampl.  of  Accommodation. 

(Emmetropia). 

10  years. 

14  D. 

15     ' 

12 

20     « 

10 

25     • 

8.5 

30     ' 

7 

35     ' 

5.5 

40     ' 

4-5 

45     • 

35 

0.5  D 

50    ' 

2.5 

1-5 

55     ' 
60    ' 
65     • 

1.5 

I 

0.5 

2-5 

3 
3.5 

70    « 

0.25 

3-75 

75     •• 

0 

4 

The  rod  optometer  is  a  very  useful  instrument  for  detecting  and 
measuring  the  amount  of  presbyopia.  It  consists  of  a  two-foot  rule, 
numerated  in  inches  or  centimeters,  or  both.    Moving  along  the  rule 


DETECTION   AND    CORRECTION   OF   ERRORS    OF    REFRACTION.      305 

there  is  a  carrier  for  test-type,  and  at  one  end  is  a  clip  holding  a  plus 
spherical  lens  of  4  D.  Through  this  convex  spherical  lens  the 
patient  should  be  able  to  at  least  read  fine  print  at  12.5  cm.  after  the 
refraction  error  has  been  corrected.  At  12.5  cm.  there  is  needed, 
without  any  lens  before  the  eye,  8  D.  accommodation.  The  convex 
lens  of  the  optometer  does  the  work  of  4  D.  accommodation,  and  the 
eyeball  supplies  the  other  4  D.  If  the  inch  system  is  used  the 
amount  of  accommodation  represented  by  12.5  cm.  or  5  inches  is  3-. 
If  a  person  does  not  read  as  close  as  5  inches  after  the  error  of  refrac- 
tion is  corrected,  ciliary  asthenia  or  presbyopia  exists  ;  the  latter  if 
the  patient  has  passed  the  age  of  forty. 

With  the  rod-optometer,  subtract  from  what  the  patient  should  do, 
what  he  can  do,  to  obtain  the  presbyopic  correction.  Thus,  a  man 
reads  at  8  inches  and  he  should  read  the  same  type  at  5  inches.  What 
glass  does  he  require  ?  Subtract  the  lesser  fraction  from  the  greater, 
3^  —  ^  =  ^.  According  to  the  dioptric  system,  patient  should  be  able 
to  read  at  12.5  cm.  and  can  read  only  at  the  more  distant  point  of 
20  cm.  What  lens  does  he  need?  12,5  cm.  is  equivalent  to  8  D. 
accommodation  (T%f~8  D.),  and  20  cm.  to  5  D.  accommodation 
{'^To'~  5  D.) ;  .3  D.  S.  is  the  lens  needed  therefore.  The  rod-optom- 
eter can  also  be  used  when  the  eyes  are  under  the  effect  of  a 
cycloplegic,  to  estimate  the  refraction  error,  which  will  be  spoken  of 
later.  The  following  plan,  that  of  Dr.  De  Schweinitz,  is  to  be  pur- 
sued in  cases  of  myopic  astigmatism  with  presbyopia.  "  A  patient 
with  simple  myopic  astigmatism  reads  best  with  a  plus  cylinder  of 
the  same  strength,  its  axis  being  reversed."  Thus,  a  patient  whose 
distant  correction  is  —  2  D,  Cyl.  Ax.  180°,  will  be  comfortable  with 
a  +  2  D.  Cyl.  Ax.  90°  for  reading.  The  convex  cylinder  with  the 
myopic  astigmatism  produces  a  myopia  of  2  D.,  in  all  meridians,  so 
he  prefers  this  lens  to  the  concave  cylinder  that  makes  him  accom- 
modate for  reading.  Simple  myopic  astigmatism  may  be  utilized  to 
ascertain  the  reading  glass  in  all  patients  past  their  thirty-fifth  year 
of  age,  provided  the  degree  is  not  too  high.  A  convex  cylinder  of 
the  same  strength  as  the  concave  one  correcting  the  astigmatism, 


306  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

with  its  axis  reversed,  is  all  that  is  required  for  the  reading-  lens.  If 
the  degree  of  myopia  thus  produced  is  too  great  for  comfortable 
reading  a  concave  spherical  lens  may  be  added  to  the  convex  cylin- 
der reducing  the  myopia  the  requisite  amount.  Thus  an  astigma- 
tism corrected  by  a  —  4  D.  C.  Ax.  1 80°  would  probably  require  a 

-  1.50  D.  S.  0  +  4  D.  C  Ax.  90°. 

If  the  degree  of  the  astigmatism  is  unequal  in  the  two  eyes,  a 
spherical  lens  is  required  to  equalize  the  refraction.  For  example  : 
R.  E.  -  5  D.  C.  Ax.  180°  ;  L.  E  -  3  D.  C.  Ax.  180°,  needs  -2D. 
added  to  the  right  eye  to  make  its  refraction  equal  to  that  of  the  left 
one.    R.  E.  -  2  D.  S.  O  +  5  D.  C.  Ax.  90°  ;  L.  E.  +  3  D.  C.  Ax.  90°. 

When  in  cases  of  compound  myopic  astigmatism,  the  myopia 
equals  several  diopters,  the  reading  lens  is  secured  by  a  sufficient 
decrease  in  the  spherical  lens  of  the  combination,  without  changing 
the  cylinder.  When  in  the  lower  forms  of  compound  myopic  astig- 
matism it  is  desired  to  increase  the  refraction  one  or  more  diopters 
the  procedure  is  somewhat  different.     Thus  if  the  combination  is 

—  .50  D.  S.  O  —  I  D.  C.  Ax.  180°,  and  the  spherical  lens  is  dropped, 
there  is  .50  D.  gained.  By  substituting  for  the  concave  cylinder, 
with  its  axis  reversed,  an  additional  i  D.  is  secured.  +  i  D.  C.  Ax. 
90°,  in  this  case  is  the  same  as  plus  1.50  D.  S.  added  to  the  combi- 
nation. If  still  more  refractive  power  is  desirable,  say  2  D.  in  all, 
+  .50  D.  S.  O  +  1  D.  C.  Ax.  90°,  gives  the  additional  amount. 

There  will  usually  appear  in  accommodation  about  4-5  degrees  of 
exophoria.  This  should  be  taken  into  account  in  the  adjustment  of 
reading  glasses ;  for  if  the  exophoria  in  accommodation  is  abolished, 
the  patient  is  given  a  practical  esophoria.  The  proper  glasses  having 
been  selected,  place  them  in  an  adjustable  trial-frame,  with  the 
optical  centers  at  the  height  of  the  pupils,  then  adjust  the  phorome- 
ter  for  exophoria  of  five  degrees,  and  bring  the  slide  of  the  instru- 
ment within  two  inches  of  the  eyes  of  the  patient.  Hold  a  card  on 
which  there  is  a  dot  upon  a  vertical  line,  in  front  of  the  instrument 
at  the  usual  reading  distance.  Now  by  the  screw  of  the  adjustable 
trial  frame,  by  altering  the  pupillary  distance,  bring  the  dots  plumb 


DETECTION   AND   CORRECTION   OF   ERRORS   OF  REFRACTION.     307 

and  the  vertical  lines  to  coincide.  Measure  the  distance  between  the 
optical  centers  of  the  lenses,  when  the  dots  are  seen  exactly  the  one 
under  the  other,  which  is  the  distance  at  which  the  centers  of  the 
permanent  reading  glasses  should  stand. 


CHAPTER  XXII 


OPTOMETERS 


There  are  many  appliances  that  have  been  brought  forward  from 
time  to  time  to  take  the  place  of  the  trial  case  of  lenses,  spoken  of 

as  optometers,  or  refractometers. 
The  advantage  claimed  for  the  ma- 
jority of  them  is  that  they  do  away 
with  the  necessity  of  changing  the 
lenses  so  frequently  before  the  pa- 
tient's eyes,  during  the  test,  and 
that  more  accommodation  is  relaxed 
as  the  strength  of  the  lens  is  grad- 
ually altered,  and  not  by  jumps  as 
we  do  when  we  replace  a  .25  D.  by 
a  .50  D.  and  so  on  in  the  trial 
frame.  The  instrument  shown  in 
the  accompanying  cut  is  that  of 
Javal  &  Bull. 

It  consists  of  two  superimposed 
discs,  one  carrying  spherical  and 
the  other  cylindrical  lenses ;  each 
disc  containing  fourteen  concave 
and  fourteen  convex  lenses,  run- 
ning from  a  +  .50  to  a  +  8  D.,  and 
from  —.50  to  —10  D.  spherical 
and  the  same  in  cylindrical  lenses. 
There  is  in  addition  on  the  reverse 
of  the  disc,  a  clip  carrying  a  plus  and 
minus  10  D.,  by  which  the  spher- 
ical lens  series  may  be  increased 
308 


Javal-Bull's  Optometer. 


OPTOMETERS. 


309 


accordingly,  and  the  different  combinations  are  easily  read  on  either 
side  of  the  discs.  The  instrument  is  so  arranged  that  either  eye  can 
be  tested  with  equal  facility.  The  lenses  are  brought  before  the  eye 
by  turning  the  large  screw-heads  seen  below  the  discs,  and  the 
cylinders  are  rotated  upon  their  axes  by  a  rack-and-pinion  movement 
seen  at  the  center  of  the  discs,  which  operates  upon  a  cog-wheel  ar- 
rangement, and  the  axes  are  indicated  by  a  pointer  upon  a  scale. 
The  whole  is  mounted  upon  a  stand  four  feet  high,  with  a  heavy  iron 
base,  and  can  be  raised  or  lowered  to  any  height.  The  lenses  can 
be  changed  very  rapidly  before  the  eye,  thus  encouraging  the  ciliary 
muscle  to  relax. 

The  fogging  method  can  be  employed  to  advantage.     A  strong 


convex  or  a  suitable  concave  lens  is  placed  before  the  sight-hole,  ac- 
cordingly, and  diminished  or  increased  by  slow  gradations  in  strength, 
until  the  best  vision  is  ascertained.  One  does  not  need  an  optometer 
of  this  kind  and  a  trial-case  both  in  the  office,  and  as  the  latter  is 
portable  it  is  in  the  whole  more  useful,  as  it  is  often  necessary  to 
take  your  lenses  to  the  patient  when  the  patient  can  not  come  to  you. 


3IO  THE   EYE,    ITS   REFRACTION   AND    DISEASES, 

The  next  cut  represents  De  Zeng's  optometer  or  refractometer, 
based  upon  the  fogging  method.  It  consists  as  shown  in  the  cut  of 
a  tubular  casing  about  2^^  inches  in  diameter  and  S^  inches  long.  It 
is  mounted  upon  the  bracket  and  pivoted  to  an  upright  pillar  which 
is  supported  below  upon  an  oxidized  iron  base.  The  front  end  of  the 
tube  is  left  open,  while  at  the  other  end  there  is  a  negative  eye-piece 
consisting  of  a  biconcave  sphere  of  20  D.  focus.  The  head  of  the 
instrument  is  provided  at  its  circumference  with  a  circular  rack, 
rotated  by  means  of  a  milled  head.  The  degree  of  rotation  is  indi- 
cated by  a  scale  with  which  cooperates  an  index  secured  to  the  upper 
side  of  the  tube.  This  scale  and  index  denote  at  any  point  of 
rotation  of  the  head  the  axis  of  the  cylindrical  lens  that  may  be 
exposed  at  the  aperture  of  the  eye-piece.  Pivoted  within  the  head 
there  are  two  revolving  discs  or  lens  carriers  having  within  them 
apertures  in  which  are  arranged  the  concave  cylindrical  lenses 
with  their  axes  at  right  angles  to  the  radii  of  the  discs  containing 
them.  These  discs  bear  the  figures  upon  their  front  surfaces  indi- 
cating the  power  of  the  lens  that  is  exposed  at  the  eye-piece.  The 
cylindrical  lenses  contained  in  the  disc  are  of  a  negative  quantity, 
and  by  combining  the  lenses  in  the  two  discs  any  strength  of  lens 
may  be  obtained.  Sliding  within  the  main  tube  of  4:he  instrument 
is  an  inner  one  constituting  the  lens  carrier,  having  in  its  rear  end 
an  achromatic  convex  lens  being  open  at  the  other  end.  This 
tube  is  graduated  upon  its  upper  surface  in  diopters  and  fractions 
thereof,  and  the  scale  so  formed  indicates  myopia  as  the  refractive 
error,  and  the  concave  spheres  for  its  correction.  The  range  of  the 
scale  is  from  zero  to  nine  diopters,  inclusive,  and  is  subdivided.  The 
graduated  circular  dial  on  the  side  of  the  cut  denotes  myopia  and 
hyperopia  or  concave  and  convex  spheres,  respectively,  ranging  from 
o  to  18  for  the  convex  and  that  of  the  concave  numbers  from  o  to 
—  1.50  inclusive,  the  continuation  of  the  latter  being  upon  the  tube 
as  has  been  noted. 

All  the  positive  effects  obtained  with  the  instrument  are  indicated 
by  the  red  figures  upon  the  circular  dial,  and  the  minus,  in  white 


OPTOMETERS.  3  I  I 

upon  the  circular  dial,  and  upon  the  tube.  There  is  an  adjustable 
indicator  on  the  upper  side  of  the  instrument,  that  has  a  white  line 
on  its  under  surface  which  cooperates  with  radiating  white  lines  on 
a  small  range  scale,  of  from  three  to  six  meters  inclusive.  The  in- 
strument may  be  arranged  to  perform  accurately  at  either  a  three-, 
four-,  five-  or  a  six-meter  range.  Attached  to  the  right  side  of  the 
tube  is  a  small  finder,  composed  of  a  small  tube  having  a  convex 
lens  at  one  end  ;  a  plane  mirror  set  at  an  angle  at  the  rear  end  and 
a  ground-glass  screen  at  its  side.  Upon  the  ground-glass  finder  are 
fixed  two  intersecting  lines  at  the  intersection  of  which  the  image  of 
the  test-card  will  appear  when  the  instrument  is  properly  directed 
towards  the  test-type.  Through  the  relative  adjustment  of  the 
achromatic  objective  and  the  stationary  negative  eye-piece,  all  the 
spherical  equivalents  from  +18  to  —9  D.  inclusive  are  obtained 
at  the  eye-piece,  and  are  recorded  upon  the  revolving  and  slid- 
ing scales.  Owing  to  the  negative  scale  being  limited  to  9  D,, 
there  are  two  auxiliary  lenses  accompanying  the  instrument,  a 
—  10  and  a  —  20  D.,  which  may  be  placed  over  the  eye-piece  when 
required,  thus  raising  the  negative  scale.  By  reason  of  its  construc- 
tion, the  instrument  has  a  magnification  of  two  and  a  third  diame- 
ters, and  in  consequence  the  test-type  to  use  with  the  instrument  are 
reduced  to  three-sevenths  of  the  size  of  Snellen's  distant  test  letters,, 
so  that  the  visual  acuity  may  be  readily  estimated  with  the  instru- 
ment. 

Method  of  Testing.  —  The  best  method  of  testing  with  the  refrac- 
tometer  is  what  is  known  as  the  fogging  method.  This  consists  in 
overcorrecting  the  hyperopic  eye  with  a  plus  sphere  and  the  under- 
correcting  of  myopia  with  a  concave  sphere,  of  such  a  strength  as  to 
render  all  the  lines  and  letters  upon  the  test-cards  blurred,  in  order 
that  the  accommodation  may  be  relaxed  and  any  hidden  error 
brought  to  light  and  measured  with  the  manifest.  It  is  claimed  for 
the  instrument  that  it  develops  more  latent  error  than  any  other  in- 
strument of  the  kind,  not  aided  by  the  use  of  a  cycloplegic,  due 
to  the  fact  that  the  illumination  is  better  than  in  any  other  method. 


312 


THE  EYE,    ITS   REFRACTION   AND    DISEASES. 


and  that  the  large  volume  of  light  stimulates  the  ciliary  muscle  to 
relax.  Experience  does  not  substantiate  this  statement.  (A  flood 
of  light  rather  stimulates  the  accommodation.)  First  set  up  the  in- 
strument in  line  with  the  test-card  and  with  range  for  which  it  is 
already  adjusted.  Next  see  that  it  is  set  at  zero  for  both  spheres 
and  cylinders,  that  no  focusing  may  exist  when  the  test  is  begun, 
and  further  that  the  test-cards  appear  in  the  center  of  the  visual  field 
of  the  refractometer,  using  the  crossed  hairs  in  the  finder  to  deter- 
mine this. 

Now  adjust  the  eye-piece  to  cover  one  eye,  while  the  brow  of  the 
other  touches  the  eye-piece  throughout  the  test.  Turn  the  focusing 
adjustment  either  to  the  right  or  to  the  left  until  the  test-card  is  seen 
the  most  distinctly,  from  which  point  turn  it  towards  higher  numbers 
among  the  red  graduations  or  lower  ones  among  the  white,  as  the 
case  may  require,  until  all  the  radiating  lines  constituting  the  fan  at 
the  top  of  the  card  are  completely  fogged.  Then  turn  the  focusing 
adjustment  slowly  back  to  the  point  at  which  the  card  was  seen  the 
best,  requesting  the  observer  to  name  the  line  or  lines  in  the  fan 
which  may  first  begin  to  clear  up,  that  the  presence  or  absence  of 
astigmatism  may  be  detected  and  its  meridians  located. 

When  all  the  lines  in  the  fan  clear  uniformly  the  registration  of  the 
highest  red  or  the  lowest  white  as  the  case  may  require,  with  which  the 
smallest  letters  on  the  test-card  are  seen  distinctly,  will  indicate  the 
nature  of  and  the  amount  of  defect  present,  and  the  kind  and  power 
of  glass  to  be  prescribed  for  its  correction,  it  being  simple  hyperopia 
if  the  numbers  are  red  and  simple  myopia  if  they  are  white.  Should 
one  or  more  of  the  lines  in  the  fan  clear  before  the  others,  the  point 
at  which  they  are  first  seen  distinctly  should  be  noted  and  the  blurred 
lines  rendered  equally  distinct  by  the  employment  of  the  cylindrical 
lenses  as  follows :  Rotate  the  head  of  the  instrument  to  a  point 
where  the  axis  register  stands  opposite  to  a  graduation  thereon 
agreeing  with  the  meridian  of  the  blurred  lines,  bring  the  cylinders 
to  the  eye-piece,  beginning  with  the  front  discs  containing  the  weak- 
est numbers.     Revolve  it  to  the  right  or  to  the  left  until  by  the  use 


OPTOMETERS.  3 1 3 


of  one  disc  or  the  other,  or  both,  a  cylindrical  power  is  obtained 
which  will  render  the  fan  uniform  to  the  eye.  After  securing  a  uni- 
formity in  the  radiating  lines  as  described,  throw  them  all  back  into 
the  fog,  that  on  bringing  them  out  again  any  under-  or  over-correc- 
tion may  be  noted.  If  under-corrected,  the  same  lines  that  came  out 
first  will  come  out  first  again,  while  if  over-corrected,  the  lines  at 
right  angles  to  those  first  appearing  to  clear,  will  clear  up  first.  If 
any  difference  exists,  correct  it  after  the  manner  described,  before 
proceeding. 

The  power  and  axis  of  the  cylinder  thus  obtained  should  be  veri- 
fied, before  completing  the  astigmatic  test,  as  follows  :  Direct  the 
attention  of  the  observer  to  the  letters  on  the  card  beneath  the  fan, 
while  a  change  in  the  strength  and  axis  of  the  cylinder  before  the 
eye  is  made  and  note  which  cylinder  and  at  what  inclination  produces 
the  clearest  definition  of  the  smallest  letters  that  can  be  read  upon 
the  card  and  is  most  acceptable  to  the  eye.  Always  prescribe  the 
weakest  cylinder  that  will  correct  the  difference  in  the  distinctness 
of  the  lines,  and  gives  the  best  vision.  The  figures  engraved  upon 
the  faces  of  the  discs  containing  the  cylinders  indicate  the  power  of 
the  lenses  exposed  at  the  eye-piece.  When  the  click  of  the  spring- 
stop  tells  the  proper  position,  they  stand  directly  opposite  the  180- 
degree  mark  on  the  axis  register  directly  beneath  them.  Should  the 
lenses  in  both  discs  be  exposed  at  the  same  time,  their  power  should 
be  combined  and  the  equivalent  expressed  as  one  lens.  In  simple 
hyperopia  always  obtain  the  highest  plus  and  in  myopia  the  weakest 
minus  that  allows  of  the  best  vision.  The  results  obtained  by  the 
use  of  this  instrument  are  equally  good  but  in  no  sense  better  than 
those  obtained  by  use  of  the  trial  case,  save  by  the  latter  method  a 
certain  amount  of  time  is  lost  in  changing  the  lenses  before  the  eyes. 

Mention  should  be  made  of  the  other  optometers  that  have  been 
devised,  those  of  Badal,  Sous,  Coccius,  Bonders,  Mile,  Scheiner,  and 
Young.  All  of  them  have  this  defect,  that  they  stimulate  the  use  of 
accommodation,  rendering  the  myopia  too  high,  as  they  operate  at 
such  a  short  range.     They  have  not  superseded  the  use  of  the  trial 


314  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

case  for  this  reason.  There  are  a  few  optometers  founded  on  the  use 
of  a  single  biconvex  lens.  By  displacing  an  object  in  relation  to  this 
lens,  the  image  of  it  can  be  formed  at  any  distance,  and  we  can  thus 
find  the  place  where  the -object  appears  distinct.  Such  were  the 
optometers  of  Donders,  Sous  and  Coccius.  Graefe  constructed  an 
optometer  of  a  Galilean  telescope  ;  myopes  have  to  shorten  their 
opera  glasses  to  see  distinctly  through  them.  By  providing  the 
opera  glass  with  a  scale  it  therefore  may  be  used  as  an  optometer, 
so  may  also  the  telescope. 

The  optometer  of  Badal  is  composed  of  a  single  convex  lens,  the 
focus  of  which  coincides  with  the  anterior  nodal  point  of  the  eyeball. 
The  position  of  the  eye  is  made  secure  by  an  eye  rest.  Along  the 
rod  on  the  other  side  of  the  lens  there  is  movable  a  diminished  copy 
of  the  Snellen's  chart.  The  retinal  image  of  the  chart  always  remains 
the  same  size  no  matter  what  the  position  of  the  chart  in  regard  to 
the  lens,  according  to  the  following  figure,  but  the  patient  can  not 
see  the  letters  equally  well  at  different  distances  from  the  lens  as  the 
light  proceeds  to  the  lens  in  more  or  less  diverging  paths  according 
to  the  position  of  the  test  card  along  the  optometer  rod.  This  will 
be  explained  more  fully  later  on.  The  visual  acuity  is  measured  by 
placing  the  test-card  at  the  principal  focus  of  the  lens  of  the  instru- 
ment, whence  the  rays  pass  through  the  lens  parallel,  and  enter  the 
eye  of  the  observer  as  if  proceeding  from  a  distance  of  twenty  feet 
or  more. 

The  Rod  Optometer  {Modification  of  the  Instrument  of  Badal).  — 
Much  information  that  aids  in  the  fitting  of  glasses  can  be  obtained 
by  means  of  the  rod  optometer.  By  its  use  the  refraction  of  the  eye 
and  the  glass  needed  to  correct  it  are  readily  ascertained.  It  consists 
of  a  two-foot  rule,  provided  with  a  clip  at  one  end  for  a  lens  and  a 
slide  movable  along  the  rule,  for  test-type.  As  a  rule  a  lo-inch  or  4 
D.  S.  lens  is  placed  in  the  clip,  and  a  diminished  Snellen's  card  used 
for  the  test-type.  By  moving  the  printed  matter  along  the  bar  the  4 
D.  lens  exercises  more  or  less  influence  over  it  according  to  its  posi- 
tion.    If  the  object  is  nearer  the  lens  than  its  principal  focus  the  light 


OPTOMETERS. 


315 


passes  through  the  lens  in  diverging  paths.  The  eye  behind  the  lens 
then  must  either  be  myopic  or  exert  its  accommodation  to  bring  such 
rays  to  a  focus  upon  its  retina.     On  the  other  hand  if  the  object  is 


~---.  b 


The  object  O  in  position  O,  O'  or  O"  is  embraced  by  parallel  rays  aa' ,  which  passing  through  the 
lens  L  come  to  a  focus  at  N,  and  diverging  include  the  image  i  of  O  upon  the  retina,  a  and  b  are  rays 
emanating  from  the  principal  focal  point  of  L  and,  therefore,  pass  out  of  it  parallel. 

beyond  the  point  of  the  principal  focus  of  the  eye-piece,  rays  emanate 
from  the  lens  in  converging  paths,  for  which  the  hyperopic  eye  is 
alone  focused.  As  the  card  is  moved  from  the  one-inch  mark  near 
the  lens  to  the  24-inch  mark  at  the  end  of  the  rule,  there  has  been 
placed  before  the  eye,  lens  strengths  ranging  from  —  36  D.  S.  to 
+  2.50  D.  S.,  and  if  the  patient  can  see  to  read  with  any  glass  within 
these  limits  there  will  be  some  position  along  the  rod  where  he  can 


Figure  II.  represents  L  placed  so  that  its  principal  focus  coincides  with  the  anterior  focal  point  of 
the  eyeball.      O,  CX  and  CX^  are  different  positions  of  the  object  and  i  its  retinal  image. 

at  least  read  some  of  the  test  letters,  and  at  the  same  time  the  degree 
of  improvement  expected  from  the  use  of  glasses  ascertained  from 
the  smallest  size  type  the  patient  reads.  If  no  reading  point  is  found 
add  four  to  eight  more  diopters  to  the  eye-piece  by  placing  the  addi- 
tional lenses  in  a  trial  frame.  If  no  reading  point  is  now  found,  there 
is  no  lens  that  will  improve  the  vision,  and  the  eye  should  be  exam- 


o 


1 6  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


ined  for  lesions.  In  high  degrees  of  hyperopia,  the  additional  lens 
may  be  necessary,  then  after  the  correction  is  ascertained  it  should 
be  added  to  or  taken  from  the  lens  in  the  trial  frame  according  to 
whether  it  is  positive  or  negative. 

More  information  can  be  gotten  from  the  rod  optometer  in  a  short 
while  than  from  any  other  one  source  alone,  and  the  more  one  uses 
it,  the  more  helpful  does  he  find  it.  There  are  two  points  from  which 
we  calculate  when  using  the  instrument ;  they  are  the  five-  and  the 
ten-inch  point.  We  reckon  from  the  first,  when  ascertaining  the 
glass  needed  for  reading  purposes,  and  from  the  latter  for  the  refrac- 
tion correction.  In  testing  poor  seeing  eyes  from  cloudy  mediae  or 
fundus  lesions  with  the  rod  optometer  we  can  often  ascertain  a  read- 
ing glass  which  gives  good  near  vision,  but  fails  to  improve  the  dis- 
tant vision.  The  patient  selects  an  abnormally  near  point  for  reading 
so  that  enlarged  retinal  images  compensate  for  loss  in  distinctness. 
A  small  astigmatic  fan  is  used  to  detect  the  presence  of  astigmatism. 
The  following  deductions  will  be  in  the  inch  system,  inasmuch  as  it 
is  customary  to  have  the  optometer  bar  graduated  in  inches.  The 
eyeball  is  focused  when  at  rest  for  parallel  rays  of  light.  It  therefore 
sees  the  smallest  test  letters  when  they  are  at  the  ten-inch  point,  or 
at  the  principal  focal  point  of  the  eye-piece.  The  ringe  of  accom- 
modation of  the  eye  before  the  advent  of  presbyopia  is  from  the  ten- 
to  the  five-inch  mark. 

Young  and  supple  eyes  can  often  see  closer  than  five  inches, 
showing  an  abundance  of  accommodation.  If  an  eye  to  see  the  test 
card  requires  that  it  be  closer  than  ten  inches  there  is  myopia  pres- 
ent, and  if  it  can  see  the  letters  further  off  than  ten  inches  hyperopia 
exists.  In  astigmatism  the  range  of  accommodation  is  found  to  be 
much  shortened.  Suppose  that  the  patient  can  see  the  small  type 
the  best  at  fifteen  inches  from  the  lens,  then  he  needs  1/10-1/15  = 
1/30  plus  lens  for  distant  seeing.  The  same  patient  can  also  see 
the  print  at  eight  inches,  but  no  closer ;  he  needs  then  for  reading 
i/5~i/8=i/i3  plus  lens.  Suppose  that  in  another  case  the  most 
distant  point  of  distinct  vision  is  eight  inches,  and  the  nearest  point 


OPTOMETERS.  3  I  7 

is  five  inches,  there  is  then  indicated  myopia  and  the  lenses  needed 
for  distant  and  near  use  are  respectively  :  1/8—1/10=1  /40  minus 
spherical  lens,  and  1/5  —  1/5  =0  D.  S.;  in  other  words  presbyopia 
has  set  in  and  no  lens  is  needed  for  reading-. 

When  testing  for  near-seeing  glasses  find  the  closest  point  at 
which  the  patient  can  read  comfortably  and  deduct  this  from  1/5. 
For  distant  glasses  ascertain  the  most  distant  point  at  which  the 
patient  can  see  to  read,  and  deduct  this  value  expressed  in  a 
fraction  with  one  as  the  numerator  from  i/io  or  vice  versa,  ac- 
cording to  which  value  is  the  major  fraction.  The  degree  of 
ametropia  may  also  be  estimated  in  the  following  manner  in  the 
metric  system.  The  greatest  distance  of  distinct  vision  minus 
the  focal  length  of  the  lens  at  the  eye-piece  divided  by  the 
common  multiple  of  these  numbers,  or  by  dividing  the  distance 
by  which  the  type  is  read  in  centimeters  into  100  cm.  to  ascertain 
the  refraction  for  that  point,  and  subtracting  this  from  the  strength 
of  the  eye-piece.  Thus,  suppose  that  the  patient  reads  best  at 
40  cm.  40  cm.  =  2.50  D.  of  refraction  ;  the  strength  of  the  lens 
of  the  instrument  is  4  D.;  4  —  2.50=1.50  D.  of  hyperopia.  Or, 
suppose  that  the  point  of  the  most  distinct  vision  is  at  10  cm. 
10  cm.  represents  10  D.  of  refraction  ;  10  —  4  =  6  D.,  the  amount  of 
myopia. 

After  the  regular  ametropia  has  been  corrected,  one  tests  for  as- 
tigmatism, especially  if  the  range  of  accommodation  is  still  shortened, 
or  if  the  patient  has  been  unable  to  read  the  finest  print  at  any  place 
along  the  rod.  The  small  astigmatic  fan  is  placed  in  the  carrier  and 
brought  from  a  distance  at  which  the  lines  are  invisible  towards  the 
eye,  moving  the  carrier  along  slowly.  If  the  lines  in  different  meridians 
come  into  view  at  different  distances  there  is  astigmatism  present. 
The  set  of  lines  that  first  come  clearly  into  view  mark  one  principal 
meridian,  that  of  least  refraction.  The  card  is  then  started  close  to 
the  lens  and  moved  slowly  away,  and  the  lines  that  first  clear  up 
noted.  These  two  sets  of  lines  should  be  at  right  angles  to  each 
other  in  cases  of  regular  astigmatism,  and  if  they  are  not  it  indicates 


3l8  THE   EYE.    ITS   REFRACTION   AND    DISEASES. 

that  the  patient  is  accommodating,  and  that  the  test  cannot  be  relied 
upon  without  the  use  of  a  cycloplegic. 

In  cases  of  simple  hyperopic  astigmatism  the  lines  occupying  one 
principal  meridian  are  seen  the  best  at  the  ten-inch  point,  and  those 
at  right  angles  to  them  best  beyond  that  point.  In  simple  myopic 
astigmatism  one  set  of  lines  is  seen  best  at  the  ten-inch  and  the  others 
nearer  the  lens  than  this  point.  In  compound  hyperopic  astigmatism 
the  lines  occupying  each  meridian  are  seen  at  least  just  as  well  if 
not  better  beyond  the  ten-inch  point,  and  in  compound  myopic  astig- 
matism all  the  lines  must  be  drawn  closer  to  the  lens  than  its  princi- 
pal focus  to  be  discerned  clearly.  In  mixed  astigmatism  one  set  of 
lines  is  seen  best  beyond  the  principal  focus  of  the  lens,  and  those  at 
right  angles  to  them  best  closer  to  the  lens  than  its  principal  focus. 

After  the  principal  meridians  have  been  located,  a  card  with  two 
sets  of  lines,  conforming  to  the  direction  of  the  principal  meridians, 
is  placed  in  the  carrier.  Suppose  that  one  set  of  lines  in  a  case  of 
compound  hyperopic  astigmatism  is  seen  best  at  twelve  inches,  which 
represents  an  error  of  1/60,  and  the  set  at  right  angles  to  them  at 
fifteen  inches,  which  represents  a  refraction  of  1/30.  The  amount  of 
astigmatism  is  equal  to  the  difference  between  the  refraction  of  the 
principal  meridians  or  i  /  60.  A  i  /60  plus  sphere  is  now  placed  before 
the  eye,  correcting  the  meridian  of  least  ametropia  and  a  1/60  cyl- 
inder combined  with  it,  with  its  axis  at  right  angles  to  the  lines  seen 
best  when  the  carrier  is  at  the  ten-inch  point.  In  a  case  of  astigma- 
tism with  the  rule  (vertical  meridian  the  least  hyperopic)  the  cross 
lines  will  be  seen  the  better  at  the  twelve-inch  point,  the  correcting 
cylinder  would  therefore  be  placed  at  ninety  degrees  at  right  angles 
to  the  better  seen  lines.  The  amount  of  astigmatism  is  ascertained 
in  the  same  manner  in  compound  myopic  astigmatism.  Thus,  sup- 
pose one  set  of  lines  is  seen  best  at  five  inches  and  the  other  set  at 
eight  inches,  the  refraction  of  the  first  point  is  i/io  (1/5  —  i/io), 
and  of  the  second  1/40  (1/8—  1/ 10),  which  equals  an  astigmatism 
of  3/40  or  1/13.  A  1/40  concave  sphere  is  now  placed  before  the 
eye  and  the  lines  moved  to  the  ten-inch  mark.     In  a  case  of  astigma- 


OPTOMETERS.  319 

tism  with  the  rule  the  horizontal  lines  will  now  be  seen  the  better, 
and  the  astigmatism  is  corrected  by  placing  a  1/13  concave  cylinder 
before  the  eye  with  its  axis  at  right  angles  to  the  lines  seen  the  better. 
In  simple  astigmatism  the  refraction  of  only  one  meridian  is  needed, 
thus : 

Suppose  that  in  a  case  of  simple  hyperopic  astigmatism  one  set 
of  lines  is  seen  best  at  ten  inches,  representing  emmetropia,  and  the 
other  set  at  right  angles  thereto,  at  twenty  inches,  representing  a  re- 
fraction error  of  1/20,  the  case  is  corrected  by  a  1/20  cylinder  axis 
at  right  angles  to  the  lines  seen  best  with  the  test  card  at  ten  inches. 
If  in  a  case  of  simple  myopic  astigmatism  one  set  of  lines  is  seen 
best  at  eight  inches,  the  astigmatism  is  corrected  by  a  1/40  concave 
cylinder,  axis  at  right  angles  to  the  lines  seen  the  better  with  the 
card  at  ten  inches. 

Suppose  that  in  a  case  of  mixed  astigmatism  one  set  of  lines 
comes  into  prominence  at  twenty  inches,  and  the  other  set  at  eight 
inches,  how  is  one  to  proceed  ?  When  the  card  is  at  twenty  inches 
it  represents  i  /  20  plus  refraction  and  when  at  eight  inches  1/40  minus 
refraction.  A  plus  or  minus  sphere  either  can  be  placed  before  the 
eye,  the  card  brought  to  the  ten-inch  mark  and  a  contrageneric  cylin- 
der of  the  strength  of  the  two  principal  meridians  combined  added  to 
the  sphere  with  its  axis  at  right  angles  to  the  better  seen  lines,  which 
will  be  at  right  angles  to  the  meridian  corrected  by  the  sphere. 

After  correcting  astigmatism,  the  test  card  (astigmatic  fan)  is 
moved  off  until  all  the  lines  fade  from  sight  and  it  is  then  brought 
slowly  towards  the  eye.  If  all  the  lines  come  into  prominence  at 
the  same  place  along  the  rod,  the  astigmatism  is  properly  corrected. 
If  the  lines  that  primarily  were  seen  the  best  come  into  prominence 
first,  the  astigmatism  is  undercorrected,  while  if  those  at  right  angles 
to  the  ones  seen  first  without  any  lens  before  the  eye  clear  up  first 
now,  the  astigmatism  is  overcorrected.  The  strength  of  the  cylin- 
drical lens  should  be  modified  until  one  is  ascertained  that  causes 
lines  drawn  in  all  meridians  to  come  into  distinctness  at  the  same 
time.     The  distant  and  near  points  of  seeing  should  then  be  ascer- 


320 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


tained  to  see  if  the  amount  of  hyperopia,   myopia  or  presbyopia 
is  properly  corrected,  using  a  card  of  small  printed  matter. 

The  Experiment  of  Scheiner. — This  consists  in  having  the  patient 
look  at  a  distant  candle  flame  through  a  disc  or  card  with  two  minute 
perforations  close  enough  together,  that  light  passing  through  each 
will  enter  the  pupil  of  the  eye.  The  light  is  placed  at  twenty  feet 
from  the  observer.  Light  passes  into  the  eyeball  through  each  of 
the  perforations,  and  if  the  eyeball  is  emmetropic,  the  light  will  meet 
in  a  common  focus  upon  the  retina  and  a  single  candle  flame  will  be 
perceived. 

A  and  b  are  parallel  rays  of  light  coming  from  some  point  in  the 
distant  candle  flame.     They  are  brought  to  a  focus  upon  the  retina,  so 

with  all  the  points  in  the  flame  and 
therefore  a  single  flame  is  seen. 
If  the  eye  is  ametropic  the  rays 
coming  through  the  two  openings 
will  not  have  a  common  focus,  but 
will  stimulate  two  separate  areas 
upon  the  retina  and  give  rise  to 
the  perception  of  two  objects.  If  the  eye  is  hyperopic,  the  rays 
from  the  two  perforations  will  reach  the  retina  befof^e  meeting  in  a 
focus,  and  two  points  of  stimulation  are  formed,  and  two  candle 
flames  seen.  Each  point  of  the  retina  stimulated  projects  its  point 
to  the  opposite  side  in  space,  so  that  the  two  flames  are  crossed,  that 


d 


6 — 


is  the  one  caused  by  the  right-hand  hole  in  the  disc  is  seen  to  the  left 
and  vice  versa.  A  red  glass  or  piece  of  celluloid  may  be  placed 
behind  the  right-hand  hole,  coloring  the  left-hand  image,  so  that 


OPTOMETERS.  32 1 

the  examiner  will  have  no  difficulty   in  telling  the    nature  of  the 
diplopia. 

y/  is  a  hyperopic  eyeball  with  Scheiner's  disc  before  it;  a  and  b 
course  of  rays  to  eyeball ;  F,  point  of  their  principal  focus ;  r,  r', 
areas  of  retinal  stimulation ;  N,  the  nodal  point  and  c,  d,  the  direc- 
tion of  projection  into  space.  The  opposite  condition  of  affairs  per- 
tains in  myopia.     The  flame  is  seen  double  but  its  images  are  not 

Disc 


crossed,  the  red  one  being  on  the  right  side  of  the  yellow  one. 
Again  if  the  disc  be  moved  to  the  right,  thus  excluding  the  right-hand 
hole  from  sending  light  into  the  eyeball,  the  right-hand  image  will 
disappear  in  myopia  and  the  left-hand  one  in  hyperopia. 

The  lettering  and  explanation  in  figure  above  are  the  same  as  for  the 
figure  on  page  320.  The  strongest  convex  or  the  weakest  concave 
spherical  lens  that  unites  the  two  images  of  the  flame  into  one  is  the 
measure  of  the  ametropia.  Astigmatism  is  detected  by  placing  the 
disc  before  the  eye  so  that  there  will  be  produced  vertical  diplopia 
and  then  measuring  the  ametropia  in  the  vertical  meridian  of  eyeball. 
The  holes  in  the  disc  must  occupy  the  vertical  direction.  Or  the 
disc  may  be  slowly  rotated  while  the  patient  watches  the  candle,  after 
the  ametropia  of  one  meridian  is  corrected.  If  there  is  no  astigma- 
tism present,  the  flame  appears  as  one  throughout  rotation  of 
disc.  To  make  the  test  still  more  accurate.  Dr.  Thompson  ar- 
ranged two  small  gas  flames  along  a  graduated  bar,  so  that  they 
could  be  made  to  approach  or  recede  from  one  another.  Viewing 
the  flames  through  the  double  perforations  of  Scheiner's  disc,  four 
flames  are  seen.     One  flame  is  then  made  to  approach  the  other  by 


322 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


sliding  it  along  the  bar,  until  three  flames  only  are  seen  by  the  coin- 
ciding of  the  two  middle  images.  The  distance  in  centimeters  sep- 
arating the  flames  is  now  read  ofl"  from  the  graduated  bar  bearing 
them,  and  the  refraction  of  the  eye  deduced  in  diopters,  by  dividing 
the  number  of  centimeters  separating  the  two  flames  into  loo  cm.,  or 
the  number  of  diopters  of  refraction  may  be  read  off  directly  from 
the  bar.  The  arrangement  of  the  ametrometer  is  shown  in  the  cut. 
If  the  two  middle  images  of  the  flame  cannot  be  made  to  fuse  with 
the  bar  of  the  instrument  horizontal  it  is  inclined  until  they  do,  and 


AMETROMETER. 


the  degree  of  inclination  denoted  on  the  scale  E  by  the  pointer  F, 
giving  the  axis  of  the  astigmatism.  The  refraction  can  be  directly 
measured  in  different  meridians  of  the  eye  by  rotating  R  through  dif- 
ferent meridians.  This  test  may  at  times  be  of  service  but  is  not  to 
be  relied  upon  to  the  exclusion  of  others,  as  the  personal  equation 
enters  largely  into  the  test,  rendering  it  more  or  less  unreliable. 
Scheiner's  test  can  be  nicely  demonstrated  by  looking  at  two  pins 
placed  one  behind  the  other,  through  the  double  perforation  of  the 
disc.     It  will  be  noticed  that  if  the  eye  is  adjusted  for  the  anterior 


OPTOMETERS.  323 

pin,  that  the  posterior  one  will  appear  double  and  vice  versa,  showing 
that  the  pin  out  of  focus  is  seen  double,  so  in  ametropia. 

The  optometer  of  Young  is  based  upon  the  experiment  of  Schei- 
ner.  It  consists  of  a  rule  upon  one  face  of  which  is  drawn  a  white 
line  upon  a  black  ground.  The  patient  looks  along  this  line  through 
a  +  10  D.  S.  lens.  In  front  of  the  lens  moves  a  small  horizontal 
rule  in  which  there  are  numerous  slits  arranged  in  groups.  The  two 
parallel  slits  act  like  the  openings  in  the  experiment  of  Scheiner. 
Each  point  of  the  line  looked  at  appears  double,  except  that  which 
is  in  focus ;  an  emmetrope,  not  using  his  accommodation  must  see 
two  lines  that  intersect  at  his  punctum  remotum,  his  artificial  far- 
point  at  10  cm.  from  the  eye,  the  principal  focal  point  of  the  lens  of 
the  instrument.  To  determine  the  refraction  of  an  eye,  a  small 
cursor  is  placed  at  the  point  at  which  the  lines  are  seen  to  intersect. 
A  dioptric  scale  placed  along  the  side  of  the  rule  permits  the  refrac- 
tion to  be  read  off  directly.  The  near-point  is  determined  in  the 
same  manner.  The  other  groups  of  slits  are  used  for  measuring  the 
refraction  in  different  parts  of  the  pupil,  as  explained  in  the  chapter 
upon  spherical  aberration.  To  test  for  astigmatism  the  instrument 
is  rotated  around  a  horizontal  axis,  so  that  the  slits  at  the  eye-piece 
occupy  different  meridians.  The  inexperienced  observer  almost  al- 
ways calls  his  accommodation  into  action  when  using  the  instrument. 
As  the  distances  are  so  small,  therefore,  better  results  are  obtained 
by  using  a  weaker  lens  at  the  eye-piece,  say  4  D.  as  has  been  noted 
in  the  modification  of  Badal's  instrument. 

Prisoptometry.  —  The  prisoptometer  consists  of  a  revolving  double 
prism  set  in  a  disc  upon  which  there  is  a  scale  of  180°  subdivided 
into  eighteen  equal  parts  of  ten  degrees  each  and  an  indicator  to 
denote  the  position  of  the  prisms.  In  the  center  of  the  disc  in  which 
the  prisms  are  set  is  an  opening  through  which  the  patient  views  the 
test  object.  The  test  object  is  a  white  disc  four  inches  in  diameter. 
This  disc  is  doubled  by  the  instrument  so  that  when  it  is  placed  at  a 
distance  of  sixteen  feet,  two  discs  are  seen  side  by  side,  appearing 
with  their  edges  just  in  contact  to  the  emmetropic  eye.     If  the  eye 


324 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


is  myopic  the  discs  seem  to  overlap  each  other,  while  if  hyperopia  is 
present  they  are  separated  from  each  other.  The  weakest  concave 
sphere  in  myopia  or  the  strongest  convex  sphere  in  hyperopia  which 

causes  the  edges  of  the  discs  to  appear 
in  contact,  is  the  measure  of  the  amount 
of  the  ametropia  present. 

When  the  prisms  in  the  instrument  are 
revolved  one  disc  appears  to  roll  around 
the  other  one.  If  there  is  no  astigmatism 
present,  the  edges  of  the  two  discs  will 
remain  in  contact  throughout  the  revolu- 
tion. If  astigmatism  is  present  they  will 
separate  or  overlap  in  some  meridian. 
The  meridians  in  which  the  discs  are 
nearest  together  and  furthest  apart  in- 
dicate the  principal  meridians  of  the  eye. 
The  scale  and  pointer  upon  the  instru- 
ment enables  one  to  read  the  inclina- 
tion of  these  meridians.  A  cylinder  of 
proper  sign  is  then  selected  that  will  in 
the  most  ametropic  meridian  cause  the 
discs  to  become  in  contact.  The  prisms 
are  then  again  rotated  to  see  if  the 
discs  remain  tangentially  to  one  another 
throughout  the  revolution.  If  they  do 
not  the  astigmatism  is  not  simple,  but 
there  is  still  needed  a  minus  or  a  plus 
sphere  as  the  case  may  be.  This  instrument  needs  the  assistance 
of  the  patient  to  give  accurate  results,  and  any  test  that  relies  upon 
the  good  will  and  intelligence  of  the  patient  is  an  inferior  one.  The 
principle  underlying  the  test  is  shown  in  the  figure  on  page  325. 

Rays  a,  ^  and  ^  come  from  the  upper  edge,  center  and  lower  edge 
of  the  test  circle  C,  and  pass  through  the  upper  portion  of  the  double 
prism.     They  are  bent  down  by  the  prism  and  entering  the  eyeball 


OPTOMETERS. 


325 


Stimulate  areas  i,  2  and  3  respectively.  The  light  that  emanates 
from  the  circle  and  passes  through  the  lower  portion  of  the  prism  is 
bent  up,  and  stimulates  the  areas  4,  5  and 
6  respectively.  As  will  be  seen,  the  areas 
of  stimulation  overlap  each  other  in  the 
myopic  eyeball ;  are  just  in  contact  in  the 
emmetropic  and  are  separated  in  the  hy- 
peropic  eyeball. 

Kinescopy.  —  Shreiner's  experiment  is 
made  the  basis  of  a  new  test  for  measur- 
ing ametropia  by  Dr.  Holth,  which  he  calls 
kinescopy.  Dr.  Holth  causes  the  rays  of 
light  to  enter  the  eye  through  a  narrow 
aperture  before  the  pupil.  An  apparent 
movement  of  the  object  looked  at  occurs 
when  the  position  of  the  aperture  is  shifted 
except  when  the  light  is  perfectly  focused 
upon  the  retina.  In  myopia  the  apparent 
movement  of  the  object  is  in  the  direction 
the  aperture  is  moved  and  in  hyperopia 
against  it.  For  astigmatism  the  move- 
ment is  most  pronounced  in  the  meridian 
of  greatest  ametropia.  The  amount  of 
ametropia  is  measured  by  lenses  placed 
before  the  eye  which  prevent  any  apparent 
movement  of  the  object  as  the  aperture  is 
shifted.  In  astigmatism  the  error  is  meas- 
ured in  both  principal  meridians.  The  dif- 
ficulty in  the  practical  test  was  to  get  rapid 
movements  of  the  opening  within  the  limits 
of  the  pupil.  Dr.  Holth  invented  an  in- 
strument which  he  called  the  kinescope  in 
which  a  slit  one  or  two  millimeters  wide  or 
an  opening  one  or  two  millimeters  in  diameter  is  given  a  rapid  move- 


326 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


ment  limited  to  three  millimeters  before  the  pupil.  The  object  looked 
at  is  either  a  white  circle  or  a  narrow  white  band  upon  a  black  back- 
ground. As  Holth  mentions,  there  is  a  direct  parallel  between  his 
test  and  retinoscopy.  Kinescopy  may  be  regarded  as  a  sort  of  sub- 
jective retinoscopy.  This  method  is  found  of  especial  value  in  eyes 
with  extremely  poor  vision  from  haziness  of  media  or  what  not.  It 
is  perfectly  applicable  in  cases  of  nystagmus  when  retinoscopy  be- 
comies  so  difficult,  and  when  the  vision  is  too  poor  to  make  the  test 
with  trial  case  of  importance. 

Ridgeway  s  Chroiitatic  Test. — This  test  is  based  upon  the  phenom- 
enon of  chromatic  aberration.     A  spherical  lens  decomposes  white 

light  that  passes  through  it  very  much  in  the 
same  way  as  does  a  prism ;  into  its  constitu- 
ent parts.  It  will  be  recalled  that  the  red 
rays  are  the  least  deviated  from  their  path, 
and  the  violet  or  blue  rays  the  most  refracted. 
If  white  light  is  intercepted  by  a  piece  of 
cobalt  blue  glass,  only  the  red  and  blue  rays 
pass  through,  the  other  spectral  colors  being 
absorbed  within  the  glass.  Ridgeway' s  chro- 
matic glass  is  shown  in  the  cut.  The  central 
portion  of  the  glass  is  thicker,  making  its  ab- 
sorbing properties  greater,  being  composed 
of  several  layers  of  blue  glass  separated  by  white  glass.  This  glass  is 
placed  before  the  eye  to  be  tested.  Through  it  the  patient  looks  at 
a  circle  of  light — a  small  hole  in  an  opaque  screen — at  a  distance  of 
twenty  feet,  placed  directly  in  front  of  his  eye.  Only  the  red  and  the 
blue  rays  pass  through  the  glass  into  the  eye.  The  blue  light  un- 
dergoes more  refraction  as  it  passes  through  the  dioptric  media  than 
the  red,  and  is,  therefore,  brought  earlier  to  a  focus.  If  the  eye  is 
emmetropic  the  red  and  the  blue  rays  cross  each  other  upon  the  ret- 
ina. The  circle  of  white  light,  therefore,  appears  purple,  a  mixture 
of  the  red  and  blue  light.  If  the  diffusion  circle  of  red  is  smaller 
than  that  of  the  blue,  the  light  will  seem  to  have  a  red  center  and  a 


OPTOMETERS. 


327 


blue  fringe,  while  if  the  blue  focusing  is  more  accurate  upon  the 
retina,  the  opposite  condition  will  pertain,  that  is,  the  circle  of  light 
will  have  a  blue  center  and  a  red  border.  In  hyperopia  the  center 
is  blue,  and  in  myopia  the  center  is  red,  with  a  border  of  the  other 
color.     The  figure  explains. 

The  size  of  the  colored  areas  depends  upon  the  amount  of  the 
ametropia.  Thus,  it  will  be  seen  by  referring  to  the  figure  that 
the  size  of  the  colored  areas  depends  upon  the  position  of  the  ret- 
ina. The  amount  of  ametropia  is  determined  by  the  lens  that  will 
correct  the  aberration,  making  the  circle  of  light  appear  a  homo- 


Diffusion 
circles  equal 


geneous  color.  This  is  a  very  delicate  test,  but  cannot  be  relied 
upon,  save  in  the  simpler  errors,  as  the  test  is  too  complicated 
to  give  very  definite  information  in  astigmatic  errors.  It  would  not 
be  so  if  the  patient  was  always  able  to  tell  the  examiner  just  how 
the  light  appears  to  him,  but  the  ability  to  do  this  varies  very  much 
with  different  individuals.  In  astigmatism  what  is  known  as  a  chro- 
moscope  is  used.  The  chromoscope  consists  of  a  card  about  two  feet 
square,  with  a  dial  divided  into  degrees.     In  the  center  of  the  dial 


> 

90° 

< 

..p 

f 

o 

v'° 

/ 

y 

-  0° 

/ 

CHROMOSCOPE 

-^ 

^ 

328  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

there  is  a  circular  opening  three  eighths  of  an  inch  in  diameter,  also 
a  rotating  ring  having  an  indicator  or  pointer  through  the  center  of 
the  opening  and  extending  across  it.  The  indicator  turns  with  the 
ring.     See  figure. 

The  card  is  placed  at  twenty  feet  in  front  of  the  patient  so  that  the 
light  from  an  Argand  burner  shines  through  the  opening.     The  eye 

not  under  test  is  covered  and  before 
the  other  one  is  placed  Ridgeway's 
glass.  If  the  light  through  the  open- 
ing appears  circular,  no  astigmatism 
exists,  but  if  the  light  appears  to  be 
drawn  out  into  an  ellipse,  astigmatism 
is  present.  In  simple  hyperopic  astig- 
matism the  circle  of  light  is  elongated, 
having  a  blue  center  and  a  red  border, 
or  is  in  the  form  of  a  cross  figure,  the  blue  extending  out  from  each 
side.  The  hand  of  the  chromoscope  is  then  rotated  to  the  longest 
axis  of  the  light  area  and  one  principal  meridian  read  off  from  the 
dial.  The  strongest  convex  or  the  weakest  concave  cylinder  that 
will  render  the  figure  of  the  light  circular  gives  the  amount  of  the 
astigmatism.  In  simple  myopic  astigmatism  the  elongated  figure 
has  a  red  center  with  blue  extremities,  the  longest  axis  indicating 
the  meridian  of  the  astigmatism.  See  figure  for  the  appearance  of 
the  light  in  different  forms  of  astigmatism. 

Dr.  Hotz  s  Astigmatism  Test.  —  This  test  depends  upon  the  ap- 
parent shape  of  a  circular  area  of  light  to  the  astigmatic  eye.  The 
drawing  on  next  page  illustrates  Dr.  Hotz's  astigmometer. 

The  instrument  consists  of  a  hard-rubber  plate  to  which  is  attached 
a  rotatory  disc  of  seven  centimeters  diameter.  In  the  disc  are  two 
small  circular  apertures,  four  millimeters  in  diameter,  and  upon  its 
edge  a  small  arrowhead.  The  centers  of  the  apertures  and  the 
head  of  the  arrow  lie  in  the  same  radius.  When  the  disc  is  rotated 
the  pointer  always  indicates  upon  the  scale  the  meridian  in  which  the 
two  apertures  lie.     Each  hole  is  covered  by  a  thin  piece  of  celluloid 


OPTOMETERS. 


329 


upon  its  posterior  side  to  give  a  uniform  illumination.  The  diffused 
daylight  from  a  window  or  the  light  of  an  Argand  burner  may  be 
used.  (The  two  apertures  may  be  replaced  by  two  circular  black 
spots  upon  a  white  ground,  giving  about  as  good  results.)  The 
bracket  should  be  fastened  to  the  wall  so  that  the  two  apertures  are 
about  on  a  level  with  the  eye  of  the  patient.  The  patient  should  sit 
at  fifteen  or  twenty  feet  distance  from  the  instrument  and  the  latter 


HOTZ'S   ASTIGMOMETER. 


should  be  turned  full  face  towards  him  with  the  indicator  at  ninety 
degrees.  The  spherical  lens  that  improves  the  vision  should  be 
before  the  eye  under  the  test  for  astigmatism.  The  patient  must 
look  steadily  at  the  two  holes  in  the  disc  to  ascertain  what  shape 
they  seem  to  have.  If  the  holes  appear  oblong  or  distorted  in  any 
manner  astigmatism  is  present.  The  direction  of  the  elongation 
marks  out  one  of  the  two  principal  meridians  of  the  eyeball.  If  the 
elongation  of  the  perforations  is  in  an  oblique  direction,  the  exact 


330  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

degree  of  inclination  can  be  ascertained  by  turning  the  disc  to  the 
right  or  to  the  left  until  the  long  axes  of  the  two  oblong  holes  are 
seen  to  be  continuous,  or  lie  in  the  same  radius  ;  the  arrow  will  then 
indicate  the  obliquity  of  the  meridian.  Astigmatism  does  not  always 
produce  an  oblong  distortion  of  the  holes.  They  may  appear  like 
half  moons,  or  diamond-shaped,  or  round  holes  with  a  light  line 
through  them  ;  sometimes  each  hole  appears  as  two,  in  which  case 
the  position  of  the  secondary  hole  indicates  the  direction  of  the 
astigmatic  elongation.  Dr.  Hotz  claims  for  the  instrument  that  it  will 
detect  astigmatism  in  92.5  per  cent,  of  cases.  The  writer's  experi- 
ence has  not  substantiated  this  claim.  As  an  adjunct  it  is  a  very 
useful  test. 


CHAPTER   XXIII 

OPHTHALMOSCOPY    IN    MEASURING    REFRACTION    ERRORS 

Objective  Methods  of  Estimating  Errors  of  Refraction.  —  In  the 
objective  examination  of  the  refraction  of  an  eye  we  employ  ophthal- 
moscopy, retinoscopy  and  ophthalmometry.  The  latter  is  of  utility 
only  in  astigmatic  errors  as  commonly  applied,  consisting  in  the 
mensuration  of  the  corneal  curves. 

Ophthalmoscopy.  —  The  estimation  of  the  sort  of  refraction  of  an 
eye  with  the  ophthalmoscope  may  be  done  either  by  the  direct  or  by 
the  indirect  method.  The  former  is  the  one  usually  employed  and  is 
upon  the  whole  the  most  reliable  and  accurate.  In  either  case  the 
accommodation  of  the  patient  must  be  in  abeyance  through  the  use 
of  a  cycloplegic  and  that  of  the  observer  voluntarily  relaxed.  The 
quickest  way  to  learn  to  relax  one's  accommodation  is  to  forcibly 
raise  the  upper  eyelids  and  try  to  stare  at  the  eye  under  examination 
as  if  you  were  trying  to  look  through  it  at  some  distant  point  behind 
the  patient's  head.  Both  eyes  must  always  be  kept  open,  as  it  is 
nearly  impossible  to  completely  relax  one's  accommodation  if  one 
eye  is  closed.  In  closing  the  eye  there  is  a  tendency  to  action  on  the 
part  of  the  ciliary  muscle  ;  as  the  two  eyes  work  together  it  is  im- 
possible to  accommodate  with  the  one  and  to  relax  accommodation 
with  the  other  one. 

Information  Gained  by  Use  of  the  Mirror  Alo7ie. — The  observer 
must  have  his  own  ametropia  corrected  by  spectacles  if  any  exists. 
He  then  seats  himself  opposite  to  and  in  front  of  the  patient  at  a 
distance  of  two  or  three  feet.  The  patient  must  look  to  the  left 
eye  of  the  observer's  head  when  the  left  eye  is  under  observation, 
and  to  the  right  when  the  right  eye  is  examined.  The  light  is  now 
reflected  into  the  eye  and  keeping  the  fundus  well  illumined  the  ob- 
server moves  his  head  from  side  to  side. 

331 


332  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

1.  If  nothing  more  than  a  red  reflex  is  seen,  or  at  most  a  blurred 
image  of  some  portion  of  the  fundus  vessels  or  optic  ner\'e,.  the  eye 
is  emmetropic  or  very  slightly  myopic.  In  the  medium  and  higher 
degrees  of  ametropia  details  of  the  fundus  are  easily  observed. 

2.  If  the  details  of  the  fundus  appear  to  move  in  the  same  direc- 
tion as  the  observer's  head  the  eye  under  examination  is  hyperopic. 

3.  If  the  vessels  are  visible  in  one  meridian  only,  and  move  with 
the  observer's  head,  there  is  hyperopia  in  one  meridian  only,  in  that 
at  right  angles  to  the  one  in  which  the  vessels  are  visible.  There  is 
then  present  simple  hyperopic  astigmatism. 

4.  If  the  image  of  the  disc  or  vessels  appears  to  move  in  a  direc- 
tion opposite  to  that  in  which  the  head  of  the  observer  is  moved, 
there  is  myopia. 

5.  If  the  details  are  seen  in  one  meridian  only,  and  they  appear  to 
move  against  the  head,  there  is  present  simple  myopic  astigmatism  ; 
the  myopic  meridian  being  at  right  angles  to  that  in  which  the  vessels 
are  visible. 

6.  If  the  fundus  details  are  seen  moving  in  one  direction  in  one 
meridian  and  in  another  direction  in  a  meridian  at  right  angles  thereto, 
there  exists  mixed  astigmatism.  This  error  is,  however,  very  diffi- 
cult to  diagnose  by  the  movement  of  vessels  or  fundus  details. 

7.  If  the  details  of  the  fundus,  instead  of  moving  regularly  and 
evenly  across  the  pupillary  area,  move  slowly  across  the  center  of 
the  pupil,  and  rapidly  and  irregularly  at  the  periphery,  giving  the 
appearance  of  rotating  bent  spokes  of  a  wheel,  there  exists  irregular 
astigmatism. 

These  tests  are  not  adapted  for  the  estimation  of  the  amount  of 
refraction  error  present,  but  are  of  diagnostic  import  only.  The 
accommodation  of  the  observer  must  be  active  to  properly  discern 
the  movement  of  the  fundus  details.  Rays  of  light  from  any  point 
of  an  illuminated  fundus  pass  out  of  the  eye  in  a  cone  of  light,  in 
which  the  rays  have  a  certain  relation  according  to  the  kind  of  refrac- 
tion present.  In  emmetropic  the  rays  pass  out  of  the  eyeball  in 
parallel  paths,  as  the  retina,  the  immediate  source  of  light,  lies  at 


OPHTHALMOSCOPY   IN   MEASURING   REFRACTION   ERRORS.        333 

the  principal  focus  of  the  emmetropic  eye.  The  light  leaves  the 
hyperopic  eye  in  diverging  paths  as  the  retina  lies  anterior  to  the 
principal  focus  of  the  dioptric  system  of  the  eyeball.  And,  in  myopia 
the  light  passes  out  in  converging  paths,  as  the  retina  lies  posterior 
to  the  principal  focus. 

The  figure  represents  an  emmetropic  eye  ;  i,  2  some  object  in  its 
fundus  ;  N,  its  nodal  point.  The  light  passes  out  of  the  eyeball  in 
cylinders  of  parallel  rays,  which  diverging  soon  leave  a  space  between 


them,  as  S,  in  which  there  are  no  rays  from  either  of  the  points  i 
and  2.  If  the  observer's  head  is  in  this  space,  it  is  evident  that  he 
can  not  get  an  image  of  the  points  i  and  2.  He  will,  however, 
receive  parallel  rays  from  some  luminous  point  of  the  object,  or  per- 
haps two  cylinders  of  rays  may  run  so  close  together  that  on  enter- 
ing the  eye  of  the  observer  may  form  an  image  of  the  portion  of  the 
object  included  by  them.  Such  an  image  is  rarely  obtained,  because 
it  requires  absolute  suspension  of  accommodation,  which  is  rarely 
met  with. 

In  hyperopia  the  rays  pass  out  of  the  eyeball  in  diverging  paths, 
from  every  point  in  the  fundus,  as  rays  a,  b  and  c.  The  cones  of 
light  composed  of  them  entering  the  eye  of  the  observer  appear  to 
emanate  from  the  points  i'  and  2',  behind  the  eyeball,  the  extremities 
of  the  virtual  image  of  the  object  1,2.  The  image  is  seen  upright. 
All  motion  of  the  fundus  details  is  judged  according  to  the  direction 
of  apparent  displacement  in  regard  to  the  plane  of  the  iris,  the  latter 
being  stationary  and  seen  at  the  same  time.  Thus,  if  a  finger  of 
each  hand  be  held  behind  one  another,  before  the  eye,  and  the  head 


334 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


moved  from  side  to  side  it  will  be  seen  that  the  front  finger  appears 
to  move  against  the  movement  of  the  head  in  regard  to  the  rear 
finger  while  the  rear  finger  moves  with  the  head  in  regard  to  the 
front  finger.     The  image  of  the  fundus  in  hyperopia  is  posterior  to 


the  iris,  and  when  the  head  is  moved  from  side  to  side  the  image 
apparently  moves  with  the  head  of  the  observer  in  regard  to  the  iris. 
In  myopia  the  image  of  the  fundus  is  formed  at  the  far-point  of  the 
eye,  where  the  returning  rays  converge  and  cross.  The  image  being 
in  front  of  the  iris  in  this  case  causes  it  to  move  in  a  direction  con- 
trary to  the  movement  of  the  head  of  the  observer.     See  figure. 


In  simple  astigmatism  we  do  not  see  any  vessels  that  run  at  right 
angles  to  the  emmetropic  meridian,  because  waves  of  light  from  their 
transverse  planes  pass  out  of  the  eyeball  in  diverging  cylinders  of 
light,  just  as  in  emmetropia,  the  same  explanation  holding  for  both, 
whereas  waves  from  the  transverse  planes  of  vessels  running  at 
right  angles  to  the  myopic  or  hyperopic  meridian  produce  in  the 


OPHTHALMOSCOPY   IN   MEASURING   REFRACTION   ERRORS.        335 

former  case  a  real  inverted  image  and  in  the  latter  a  virtual  erect 
imaofe  of  the  vessels. 

There  follows  then  the  same  rule  of  movement  that  pertains  in 
simple  hyperopia  or  myopia.  In  cases  of  common  myopic  astigma- 
tism if  the  observer  uses  his  accommodation,  vessels  at  right  angles 
to  the  most  myopic  meridian  will  be  distinctly  seen  much  closer  to  the 
patient's  eye  than  those  in  the  opposite  direction.  Rays  from  the 
transverse  planes  of  the  former  converge  and  form  an  inverted 
image  much  sooner  than  do  those  from  the  latter.  In  compound 
hyperopic  astigmatism  we  find  that  for  the  vessels  at  right  angles 
to  the  most  hyperopic  meridian  more  accommodation  is  required 
than  for  those  in  the  opposite  direction  from  a  given  distance. 

A  greater  extent  of  the  former  than  of  the  latter  vessels  is  however 
at  the  same  time  visible.  Rays  from  the  former  are  more  divergent, 
and  the  cones  of  light  take  longer  to  separate.  In  mixed  astigmatism 
images  of  the  vessels  may  be  seen  sometimes  inverted  and  some- 
times erect  according  to  the  meridian  through  which  the  rays  emerge, 
and  varying  with  the  observer's  accommodation.  The  details  are 
more  visible  than  in  emmetropia  but  are  nevertheless  very  indefinite 
(Morton).  The  manner  of  estimating  the  amount  of  refraction  error 
by  the  direct  method  will  now  be  considered.  The  patient  and  the 
physician  seat  themselves  as  for  the  direct  examination  of  the  fundus 
of  the  eye.  The  accommodation  of  the  patient  must  be  relaxed  by 
the  use  of  a  cycloplegic,  the  pupil  being  expanded  by  the  same  drug. 
The  accommodation  of  the  observer  is  voluntarily  relaxed.  His  re- 
fraction error  must  be  corrected  by  proper  spectacle  lenses  or  by  re- 
volving back  of  the  sight-hole  of  the  ophthalmoscopic  mirror  the 
appropriate  lens  strength.  The  former  is  the  better  method,  as  then 
no  deductions  need  be  made  from  the  reading  of  the  ophthalmoscope, 
after  the  completion  of  the  test  to  ascertain  the  amount  of  refraction 
error  present  in  the  eye  under  observation.  With  no  lens  behind 
the  sight-hole  of  the  mirror  the  examiner  throws  the  light  into  the 
patient's  eye,  and  then  moves  closer  and  closer  towards  the  eye  until 
the  ophthalmoscopic  mirror  is  nearly  in  contact  with  the  cornea.     If 


33^ 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


the  observer  is  exerting  no  accommodation  there  will  be  seen  nothing 
save  a  very  blurred  image  of  the  fundus  or  only  a  red  glare,  unless 
the  eye  under  examination  is  emmetropic,  in  which  case  the  details 
of  the  fundus  will  be  distinctly  seen.  In  emmetropia  the  vessels  and 
the  disc  can  not  be  seen  furthermore,  if  the  accommodation  of  the 
observer  is  exerted,  or  if  a  plus  or  minus  lens  is  revolved  behind  the 
sight  hole  of  the  mirror. 

The  dotted  lines  in  the  figure  represent  the  path  of  light  from  the 
mirror,  illuminating  the  fundus  of  the  eyeball  B,  over  the  area  ad  ;  O 
is  an  object  within  that  area  from  which  light  emanates  along  the 
continuous  lines.  The  rays  from  the  upper  end  of  object  O  pass 
out  of  the  eye  parallel  as  xx\  and  are  focused  at  the  O'  below  in  the 


eye  B'.  Rays  yy  emanate  from  lower  portion  of  object  and  are 
focused  in  £'  above.  As  the  retina  of  £  lies  at  the  principal  focus 
of  the  dioptric  system,  the  light  passes  out  in  parallel  paths  and  as 
£'  is  emmetropic  they  are  focused  accurately  upon  the  retina  of  £' 
without  the  need  of  accommodation.  The  observer's  eye  therefore 
sees  distincdy  the  details  within  the  eye  E.  Any  lens  back  of  the 
mirror  would  of  course  spoil  the  image,  as  the  rays  passing  through 
it  would  have  a  different  relation  imparted  to  them  and  they  would 
no  longer  be  focused  upon  the  retina  of  £\ 


OPHTHALMOSCOPY   IN   MEASURING   REFRACTION   ERRORS.        337 

Test  for  Myopia.  —  In  myopia  no  details  of  the  fundus  of  the  ob- 
served eyeball  can  be  seen  with  or  without  accommodation.  It  is 
necessary  to  place  a  concave  spherical  lens  behind  the  sight-hole  of 
the  mirror  in  order  that  a  view  of  the  fundus  may  be  gotten.  The 
returning  rays  in  M  are  convergent  and  such  rays  are  focused  an- 
terior to  the  retina  of  the  normal  eye.  Accommodation  on  the  part 
of  the  observer  still  further  shortens  the  focus.  A  concave  lens 
causes  the  rays  to  diverge  and  when  they  are  rendered  parallel  by 
the  proper  lens  strength,  the  observer  sees  distinctly  the  details  of 
the  fundus  of  the  observed  eye,  as  the  former  is  adjusted  for  parallel 
rays  of  light.     The  minus  lens  back  of  the  ophthalmoscope  renders 


Observer 


Observed 


the  eye  under  test  a  little  more  hyperopic  each  time  its  strength  is 
increased,  until  the  amount  of  hyperopia  produced  is  equal  to  the 
amount  of  the  myopia  originally  present. 

The  ophthalmoscope  should  be  held  against  the  side  of  the  nose 
with  the  mirror  perfectly  vertical  and  the  lenses  are  revolved  into 
place  by  turning  the  small  milled  wheel  at  the  side  of  the  in- 
strument with  the  index  finger,  turning  it  to  the  light  to  get 
plus  lenses  in  and  to  the  left  for  the  minus  lenses.  The  instrument 
should  be  so  constructed  that  one  may  know  what  lens  is  in  place 
without  taking  the  instrument  down  from  the  eye.  Morton's  im- 
proved ophthalmoscope  is  the  most  convenient.  The  figure  above 
shows  how  minus  lenses  correct  myopia  and  indicate  the  amount 
of  error. 

Rays  a  and  b  proceed  from  eye  M,  in  converging  paths.     Minus 


338  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

lens  L  renders  them  parallel  2lS  c,d\  they  are  then  brought  to  a  focus 
upon  the  retina  of  the  eye  E. 

In  hyperopia  the  details  of  the  observed  eyeball  may  be  seen 
clearly  only  when  the  observer  uses  his  accommodation  or  when  he 
revolves  a  convex  sphere  behind  the  sight-hole  of  his  ophthalmo- 
scope. The  diverging  paths  of  light  as  they  pass  out  of  the  observed 
eye  into  the  observer's,  are  rendered  parallel  by  accommodation,  but 
if  the  ciliary  muscle  is  at  rest  come  to  a  focus  posterior  to  the  retina 
and  only  a  blurred  picture  of  the  details  of  the  fundus  of  the  observed 
eye  is  gotten.     See  figure  below. 

Rays  a,  b  and  a'  b'  leave  the  hyperopic  eyeball  from  points  x  and 
y  of  the  fundus,  respectively,  in  diverging  paths.     They  are  rendered 


Observed 


parallel  by  the  convex  lens,  and  are  then  focused  by  the  dioptric 
media  of  the  eye  E,  upon  its  retina,  giving  it  a  clear  picture  of  the 
fundus  of  H. 

Astigmatism  can  be  diagnosed  from  the  apparent  shape  of  the 
optic  papilla,  which  instead  of  round  appears  more  or  less  oval.  In 
the  erect  image  (direct  method)  the  long  axis  of  the  oval  corresponds 
with  the  meridian  of  the  greatest  refraction,  that  is,  in  myopia  the 
meridian  of  greatest  myopia  and  in  hyperopia  the  meridian  nearest 
emmetropia  (least  hyperopia).  As  a  rule  the  long  axis  of  the  oval  is 
vertical.  In  the  inverted  image  the  direction  of  the  oval  is  at  right 
angles  to  the  meridian  of  the  greatest  refraction,  provided  the  objec- 
tive lens  is  nearer  the  eye  than  its  own  focal  length.     Astigmatism 


OPHTHALMOSCOPY   IN   MEASURING   REFRACTION   ERRORS.        339 

is  furthermore  suspected  when  an  undilating  retinal  vessel  is  seen 
clear  and  blurred  in  parts.  This  condition  is  not  to  be  confused 
with  an  effusion  into  the  retina.  It  is  differentiated  by  the  fact  that 
a  concave  or  a  convex  lens  back  of  the  sight-hole  of  the  ophthalmo- 
scope will  bring  into  distinctness  the  blurred  portions  of  the  vessel, 
which  would  not  be  the  case  if  an  exudate  was  present.  The  appear- 
ance of  a  retinal  vessel  in  astigmatism  may  well  be  imitated  by 
looking  at  a  wavy  line  through  a  strong  cylindrical  lens.  The  quan- 
titative test  of  astigmatism  by  the  direct  method  is  to  find  the  lens 
that  will  clear  up  the  vessel  in  different  directions.  The  small  vessels 
about  the  macular  region  are  the  best  ones  to  focus  upon.  The  lens 
that  brings  the  vessel  running  crosswise  into  clear  view  denotes  the 
refraction  of  the  eye  at  right  angles  to  the  course  of  the  vessel,  and 
the  difference  in  the  strengths  of  lenses  needed  to  clear  up  a  vessel 
in  its  vertical  and  horizontal  portions,  or  in  any  other  two  directions 
at  right  angles  to  each  other,  represents  the  amount  of  the  astigma- 
tism. Thus  a  vessel  that  runs  up  and  down  is  seen  best  with  a  plus 
2  D.  S.,  and  when  it  runs  crosswise,  best  with  a  plus  i  D.  S.  The 
amount  of  astigmatism  is  2  —  1  =  1  D.,  and  the  correc:ion  is  written 
as  follows  : 

+  I  D.  S.  O  +  I  D.  C.  Ax.  90°.  - 

The  above  is  a  case  of  compound  hyperopic  astigmatism.  If  minus 
lenses  are  needed  for  both  meridians,  the  case  is  one  of  compound 
myopic  astigmatism,  and  mixed  when  a  minus  lens  is  needed  for  one 
and  a  plus  for  the  other  principal  meridian.  The  mensuration  of  the 
refraction  error  is  not  difficult  in  simple  hyperopia  or  myopia,  but  in 
astigmatism  and  especially  if  the  principal  meridians  are  oblique,  the 
test  is  very  difficult  and  very  few  are  masters  of  it  enough  to  rely 
upon  it.  In  astigmatism  it  is  very  difficult  to  measure  closer  than 
I  D.  Abroad  this  method  of  correcting  refraction  errors  is  used  a 
great  deal,  but  in  this  country  where  we  care  for  accurate  results  in 
refraction  work,  and  correct  even  as  low  as  .12  D.,  ophthalmoscopic 
correction  is  not  considered  of  very  great  importance  by  the  refrac- 


-40  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

tionist.  By  ophthalmoscopy  the  principal  meridians  are  denoted  by 
the  direction  of  the  best  and  poorest  seen  vessels  in  the  fundus  of 
the  eye,  without  any  lens,  or  with  the  weakest  one  that  clears  up  the 
vessels  running  in  any  given  direction. 

Indirect  Method. — After  ascertaining  the  direction  that  the  vessels 
of  the  fundus  of  the  eye  seem  to  move,  when  the  observer  moves  his 
head  from  side  to  side,  the  objective  lens  is  held  before  the  eye.     If 
the  objective  lens  be  made  to  approach  and  to  recede  from  the  eye, 
it  will  be  noticed  that  in  the  emmetropic  eye  there  is  no  change  in 
the  size  of  or  shape  of  the  optic  disc.     If  on  moving  the  lens  back- 
ward and  forward  there  is  a  change  in  the  appearance  of  the  disc,  we 
are  dealing  with  ametropia.     In  hyperopia  it  will  be  seen  that  on 
withdrawing  the  lens  from  the  eye  under  observation  that  the  image 
of  the  disc  becomes  smaller  (small  or  short  eyeball,  smaller  image) 
and  in  myopia  that  the  image  apparently  increases  In  size  (large  eye, 
larger  image).     The  explanation  of  this  is  found  in  the  fact  that  the 
relative  sizes  of  image  and  object  are  to  each  other  as  their  distances 
from  the  lens.     To  find  the  distance  of  an  image  from  the  lens  we 
have  the  following  formula  :   \\d=  \\f—  i/A  in  which  d  is  the  dis- 
tance of  the  image  from  the  lens,  f  the  focal  length  of  the  lens,  and 
D  the  distance  of  the  object  from  the  lens.     Let  f'=\  cm.     In  em- 
metropia,  the  light  issuing  from  the  fundus  of  the  eye  passes  out  in 
parallel  paths,  as  if  emanating  from  an  object  situated  at  an  infinite 
distance.     It  is  of  this  supposed  object  that  we  get  an  image  of  the 
disc  by  means  of  the  objective  lens.     In  emmetropia  it  matters  not 
where  the  lens  is  held,  the  parallel  rays  go  to  form  the  image  at  the 
principal  focus  of  the  lens,  the  relative  distances  of  the  image  and  the 
object  from  the  lens  remain  constant,  therefore  the  size  of  the  image 
does  not  change  as  the  lens  is  withdrawn.     In  hyperopia  rays  emerge 
from  the  eyeball  as  if  emanating  from  an  object  at  a  certain  distance 
behind  the  eye.     It  is  of  this  virtual  object  that  we  get  an  image  with 
the  convex  lens  held  close  to  the  patient's  eye.     Suppose  the  lens  to 
be  held  at  6  cm.  from  the  object,  the  distance  of  the  image  from  the 
lens  is  according  to  formula  \\d=  i /4  —  i /6  =  i / 1 2,  or  d  =  12  cm. 


OPHTHALMOSCOPY    IN    MEASURING   REFRACTION    ERRORS.        34 1 

The  ratio  between  the  distance  of  the  image  and  object  is :  dj D 
=  12/6  =  2. 

If  we  now  withdraw  the  lens  to  12  cm.,  the  distance  of  the  image 
from  the  lens  will  be  :  i/rtf=  1/4—  1/12  =  1/6,  or  d  =  6cm.;  the  ratio 
in  this  case  is  dj D  =  6/12  =  1/2.  The  ratio  of  the  distance  of  the 
image  from  the  lens  as  compared  with  that  of  the  object  from  the  lens 
being  greater  in  the  first  case  than  in  the  second,  so  is  the  size  of  the 
image.  In  myopia  rays  emerge  from  the  disk  converging,  and  form  at 
a  certain  distance  in  front  of  the  eye  a  real  inverted  image  of  the  disc. 
This  image  is  to  be  regarded  as  the  object  of  which  we  get  an  image 
when  the  objective  lens  is  held  close  to  the  patient's  eye.  In  this 
case  the  object  and  the  image  are  on  the  same  side  of  the  lens.  The 
object  being  on  the  opposite  side  of  the  lens  from  which  the  rays 
proceed,  it  is  customary  to  make  ijD  negative,  so  that  the  same 
formula  may  apply  in  each  case.     The  formula  then  becomes 

ild=ilf-{-ilD)=ilf+ilD. 

If  the  lens  is  placed  1 2  cm.  nearer  the  eye  where  the  image  would 
be  formed  we  have  the  image  formed  at  3  cm.  from  the  lens. 

ijd  =  1/4  +  1/12  =4/12  =  1/3,  d=  3  cm.     Ratio  d/D=  1/4. 

If  we  now  withdraw  the  lens,  that  is  towards  the  object,  but  from  the 
eye  until  it  is  6  cm.  from  the  former,  the  distance  of  the  image  will  be 
nearly  two  centimeters,  given  a  ratio  of  1/3.  As  the  ratio  is  greater 
in  the  second  case,  so  is  the  image.  This  explanation  holds  good  so 
long  as  the  objective  lens  is  not  withdrawn  beyond  the  far  point  of  the 
eye  plus  its  own  focal  length  ;  for  hyperopia  so  long  as  the  focal  power 
of  the  lens  is  greater  than  the  degree  of  hyperopia.  The  latter  is 
always  the  case  as  the  objective  lens  is  usually  of  a  three-inch  or  less 
focal  distance,  save  in  acquired  hyperopia  after  the  removal  of  the 
crystalline  lens.  In  very  high  degrees  of  myopia,  however,  if  the  lens 
be  further  from  the  eye  than  the  aerial  inverted  image  of  the  fundus, 
plus  its  own  focal  length,  the  erect  image  of  the  fundus  is  formed  be- 
tween the  lens  and  the  observer,  the  variations  in  the  size  of  which 


342  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

are  subjected  to  the  same  rules  as  those  for  the  inverted  image  in 
hyperopia  (Morton). 

The  Quantitative  Test  of  Refraction  by  the  Indirect  Method  of 
Ophthabnoscopy.  —  If  we  know  the  distance  of  the  image  of  the  fun- 
dus of  an  eye  fromthe  objective  lens,  and  the  focal  length  of  the  latter, 
we  can  without  difficulty  deduce  the  refraction  of  the  eye.  The 
method  of  measuring  the  refraction  of  an  eye  by  the  indirect  method 
of  ophthalmoscopy  is  that  of  Schmidt-Rimpler.  The  method  has 
never  become  very  popular.  The  observer  makes  himself  artificially 
myopic  by  placing  a  convex  lens  back  of  the  sight-hole  of  the  ophthal- 
moscope. A  convex  5  D.  S.  is  the  one  generally  used,  which  makes 
the  eye  of  the  observer  just  5  D.  M.  if  he  has  an  emmetropic  eye. 
Such  an  eye  cannot  see  anything  distinctly  further  off  than  the  dis- 
tance of  its  own  far-point,  which  in  this  case  lies  at  20  cm.  in  front 
of  the  eye.  The  observer  then  throws  the  light  into  the  eye  under 
test.  An  objective  lens  of  known  strength,  preferably  a  10  D.,  as 
that  strength  makes  the  deduction  easier,  is  held  before  the  eye. 

From  the  usual  distance  at  which  the  fundus  of  an  eye  is  examined 
the  artificially  myopic  observer  does  not  see  anything  but  a  red  glare 
from  the  chorioid.  As  he  moves  his  head  closer  to  the  patient  the 
image  of  the  fundus  comes  clearly  into  view,  when  he  is  at  a  distance 
from  it  equal  to  the  distance  of  his  far-point,  that  is  at  20  cm.  from 
the  image.  Knowing  the  distance  of  his  far-point  and  the  distance 
of  his  eye  from  the  objective  lens,  which  latter  is  indicated  upon  a 
tape  line  that  the  observer  holds  stretched  between  the  ophthal- 
moscope and  the  objective  lens,  he  can  ascertain  the  position  of 
the  image  in  regard  to  the  objective  lens.  The  image  of  the  fun- 
dus is  situated  at  a  greater  or  a  less  distance  from  the  objective  lens 
according  to  the  state  of  refraction.  If  we  use  a  convex  objective 
lens  of  10  D.  the  inverted  image  of  the  emmetropic  eye  will  lie  at 
ten  centimeters  from  the  lens,  that  is  at  its  principal  focus,  as  rays 
of  light  pass  out  of  the  emmetropic  eye  parallel.  The  image  of  the 
fundus  of  the  hyperopic  eye  will  be  further  away  and  that  of  the 
myopic  eyeball  nearer  the  lens  than  10  cm.     Each  centimeter  nearer 


OPHTHALMOSCOPY    IN    MEASURING   REFRACTION    ERRORS.        343 

the  lens  adds  one  diopter  of  myopia,  and  each  centimeter  further  off 
I  D.  of  hyperopia.  For  example,  if  the  image  is  situated  at  6  cm. 
from  the  lens  there  is  4  D.  of  myopia  (10  —  6  =  4  D.);  if  20  cm.  away 
20  —  10  =  10  D.  of  hyeropia  and  so  on. 

The  Application  of  the  Test. — The  observer  is  at  30  cm.  from 
the  objective  lens,  the  furthest  point  at  which  he  can  distinctly  see 
the  image  of  the  fundus.  What  is  the  refraction  of  the  eye? 
30  cm.  (distance  of  observer  from  lens)  —  20  cm.  (distance  of  image 
from  observer's  eye)  =  10  cm.  (distance  of  image  from  objective  lens). 
As  10  cm.  is  the  focal  distance  of  the  lens  in  use,  the  eye  under  test 
is  emmetropic,  inasmuch  as  the  image  of  the  fundus  is  formed  at  the 
principal  focus  of  the  objective  lens.  This  method  is  not  practical 
in  astigmatic  errors  and  is  less  accurate  than  the  direct  method.  For 
this  method,  as  well  as  for  the  direct,  the  accommodation  of  the  ob- 
server's eye,  as  well  as  that  of  the  patient,  must  be  in  abeyance. 


CHAPTER   XXIV 


RETINOSCOPY 


Retinoscopy,  skiascopy  or  the  shadow  test,  is  the  most  accurate 
and  the  most  reliable  test  at  our  disposal  for  detecting  and  estimating 
the  amount  of  refraction  error  of  an  eye.  It  is  independent  of  the 
good  will  and  intelligence  of  the  patient.  It  does  not  rely  upon  the 
answers  of  the  patient  as  does  the  subjective  test  with  the  trial  case, 
and  the  accuracy  of  the  test  is  not  influenced  by  the  presence  of  an 
error  of  refraction  in  the  observer,  so  long  as  he  can  see  well  enough 
to  discern  the  movement  of  light  and  shade  in  the  pupil  of  the  ob- 
served eye.  This  method  of  examining  ocular  refraction  was  de- 
scribed by  Cuignet  in  1873  and  called  by  him  keratoscopy.  Parent 
especially  developed  the  method  and  was  the  first  who  gave  the  cor- 
rect explanation  of  the  test.  By  retinoscopy  we  measure  the  amount 
of  myopia  resident  in  the  eye  or  that  produced  by  a  convex  spherical 
lens  placed  before  the  eye,  by  ascertaining  the  position  of  its  far- 
point.  Light  is  reflected  into  the  eye  under  examination  from  a 
mirror ;  the  illuminated  area  in  the  eye  is  seen  to  mfove  as  the  mirror 
is  tilted,  and  according  to  the  direction  of  this  movemont,  which  varies 
with  the  position  of  the  observer  in  regard  to  the  far-point  of  the  eye, 
the  latter  is  located. 

If  the  observer  is  nearer  to  the  observed  eye  than  its  far-point,  the 
movement  of  light  in  the  eye  is  in  one  direction,  while  if  he  is  further 
away  than  the  far-point  the  movement  is  in  the  opposite  direction. 
The  test  may  be  performed  with  either  a  concave  or  plane  mirror. 
There  are  many  kinds  of  retinoscopes  on  the  market.  The  sight- 
hole  of  the' mirror  should  be  very  small,  not  exceeding  1.5  mm.  in 
diameter,  and  made  by  scratching  the  amalgam  off  from  the  back  of 
the  mirror  in  preference  to  boring  a  hole  through  the  mirror.  If 
the  sight-hole  is  bored  through  the  glass,  one  is  annoyed  by  reflection 

344 


RETINOSCOPY. 


345 


from  the  sides  of  the  bore,  unless  they  are  kept  well  blackened.  The 
metal  backing  to  the  mirror  should  be  very  thin,  so  that  there  is  no 
room  for  the  collection  of  dust.  The  mirror  should  be  provided  with 
an  arrangement  so  that  its  reflecting  surface  may  be  diminished  or 
increased,  as  a  different  size  mirror  is  often  needed  in  different 
stages  of  the  test.     The  one  shown  in  the  cut  is  that  devised  by  Dr. 


Jackson  ;  it  is  as  cheap  as  any  and  at  the  same  time  the  most  con- 
venient one  to  be  had.  In  figure  no.  i  only  a  small  central  area 
of  the  mirror  is  exposed,  while  in  figure  no.  2,  the  entire  mirror. 

If  the  far-point  of  the  eye  under  examination  lies  at  the  principal 
focus  of  the  convex  lens  before  it,  the  eye  is  emmetropic.  The  light  is 
reflected  into  the  eye,  the  fundus  is  illumined,  the  returning  rays  pass 
out  of  the  eyeball  into  the  lens  before  it  parallel  and  converging  are 
brought  to  a  focus  at  the  principal  focus  of  the  lens.  This  point 
is  the  far-point  of  the  eye  rendered  myopic  by  the  convex  lens  be- 
fore it.  Therefore  emmetropia  exists  if  the  far-point  of  the  eye 
rendered  myopic  lies  at  a  distance  from  the  lens  equal  to  its  own 
focal  distance.  The  fact  that  the  returning  rays  of  light  from  the 
eyeball  are  focused  at  the  principal  focus  of  the  lens  is  evidence  that 
they  entered  the  lens  parallel,  emitted  thus  from  the  eye. 


346  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

a  and  b  are  rays  passing  out  of  eyeball ;  F,  focus  of  a'b'  through 
L.  de=  I  m.  The  strength  of  L  is  known  to  be  i  D.  Therefore 
a'b'  are  parallel  on  entering  L.     In  this  case  the  eye  is  rendered   i 


D.  M.     Hyperopia  is  denoted  if  it  takes  a  stronger  lens  than  a  plus 
I  D.  to  render  the  eye  under  observation  i  D.  myopic. 

Light  emanates  from  the  illuminated  fundus  of  the  eye  H,  in 
diverging  paths  as  ab.  Portion  /'  of  the  convex  spherical  lens  L, 
renders  the  rays  parallel,  and  therefore  corrects  the  hyperopia,  por- 
tion /  brings  the  rays  rendered  parallel  to  a  focus  at  a  meter's  dis- 
tance.    The  strength  of /is  then  known,  being  i  D.;  the  strength  of 


-i-4  D.  S. 


L  is  known,  having  been  selected  by  the  examiner — in  this  case  it  is 
supposed  to  be  a  +  4  D.  S.  lens.    The  amount  of  hyperopia  is  then  : 

4-iD.  =  3D. 

The  far-point  of  the  myopic  eyeball  in  retinoscopy  is  called  the 
pomt  of  reversal.  It  is  likewise  the  external  conjugate  focus  of  the 
dioptric  system  of  the  eyeball.  The  point  of  reversal  is  so  called, 
because  when  the  observer  is  nearer  the  eye  than  this  point  the 


RETINOSCOPY.  347 

illuminated  area  in  the  eye  appears  to  move  in  one  direction  and 
when  beyond  this  point  the  movement  is  the  reverse,  as  the  skia- 
scope is  turned  about  its  axis.     The  catoptric  image  of  the  light  is 
called  the  immediate  source  of  light  to  the  eye  un- 
der observation  in  contra-distinction  to  the  original  ^ 
source  of  light  to  the  mirror.     The  light  that  illu-      ^^''""^iji^^ 
mines  the  eye  is  the  reflected  image  of  the  original       1 
source  of  light.     The  original  source  of  light  should       ' 
be  shaded,  and  the  room  made  perfectly  dark  to  ex- 
clude all   extraneous  light.     The   most  convenient 
light-shade  is  that  of  Dr.  Thorington  shown  in  the 
cut.     It  consists  of  an  iris  diaphragm  attached  to  a 
blackened  asbestos  chimney.     The  size  of  the  open- 
ing in  the  shade  is  regulated  by  a  small  lever  that 
projects  from  the  side  of  the  diaphragm.  An  Argand 
burner  is  the  most  convenient  source  of  light.     It 
should  be  fastened  to  an  upright  or  adjustable  wall 
bracket,  so  that  the  height  of  the  light  can  be  altered, 
and  drawn  closer  or  pushed  further  off  as  the  observer  desires. 

In  the  great  majority  of  cases  under  fifty  years  of  age  it  is  neces- 
sary to  employ  a  cycloplegic,  especially  in  astigmatism,  as  it  is 
impossible  to  accurately  measure  a  quantity  that  is  apt  to  change 
from  time  to  time  during  the  test.  To  apply  retinoscopy  with  the 
greatest  ease  furthermore  needs  a  pupil  moderately  dilated.  Like 
other  methods  it  will  not  give  as  accurate  results  if  the  pupil  is  very- 
narrow,  and  on  account  of  aberration  and  irregular  astigmatism  that 
usually  exists  near  the  margin  of  the  lens  and  the  cornea,  very  wide 
dilatation  of  the  pupil  introduces  difficulties.  The  pupil  should  never 
be  less  than  4  mm.  in  diameter.  If  this  is  the  case  in  the  elderly 
cocaine  may  be  used  as  the  mydriatic. 

If  a  mydriatic  is  not  used  for  some  reason  or  other  (as  in  eyes  in 
which  one  fears  an  attack  of  glaucoma)  the  accommodation  is  ren- 
dered fixed,  and  relaxed  to  a  certain  extent  by  having  the  patient  look 
at  large  letters  hung  at  a  distance  of.  twenty  feet,  in  a  partially 


348  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

darkened  room,  especially  if  the  eye  not  under  the  test  that  sees  the 
letters  is  fogged  by  a  strong  convex  lens.  The  patient  should  look 
a  litde  to  one  side  of  the  mirror  so  that  the  pupil  will  be  as  large  as 
possible. 

Description  of  the  Test  with  a  Plane  Mirror. — Let  us  begin  with 
an  emmetropic  eye.  The  examiner  reflects  the  light  into  the  eye  and 
turning  the  mirror  from  side  to  side  (about  a  vertical  axis)  notices 
that  the  light  area  in  the  eye  moves  with  the  rotation  of  the  mirror, 
and  with  the  light  on  the  face  of  the  patient,  that  is  when  the  mirror 
is  turned  to  the  right  the  light  moves  to  the  right  in  the  eye  as  well 
as  upon  the  face  of  the  patient.  The  apparent  movement  of  the 
light  in  the  eye,  that  is  as  it  appears  to  the  observer,  is  the  same  as 
the  real  movement  of  light  in  the  eye  under  observation,  that  is  as  it 
really  moves  across  the  fundus  of  the  eye,  and  would  appear  to  an 
observer  if  he  were  behind  the  eye  and  looking  through  the  sclera  and 
chorioid.  The  reason  that  the  light  moves  with  the  rotation  of  the 
mirror  is  as  follows  :  When  the  mirror  is  tilted  to  the  left  the  light  is 
reflected  to  the  left  and  vice  versa. 

In  the  figure  ( i )  is  the  image  of  the  original  source  of  light  when 
the  plane  mirror  is  in  position  (i) ;  the  light  entering  the  eye  as  if  it 
originated  at  image  (i),  illuminates  the  fundus  over  the  area  (i). 
When  the  mirror  is  rotated  or  turned  up  to  position  (2),  in  the  direc- 
tion of  the  arrow,  the  immediate  source  of  light  descends  to  (2),  illu- 
minating the  fundus  now  at  (2).  The  light  in  the  eye  moves  in  the 
same  direction  as  the  mirror  and  appears  to  the  observer  to  move  in 
the  direction  it  does,  as  the  rays  that  return  from  the  emmetropic  eye 
never  change  their  relation  to  each  other,  remaining  parallel,  and 
those  that  emerge  from  above  remain  above  until  they  enter  the  eye 
of  the  observ^er.  In  emmetropia,  then,  the  light  appears  to  move  in 
the  direction  of  rotation  of  the  mirror  or  with  the  light  upon  the  face 
at  all  distances  from  the  eye.  The  same  is  true  in  hyperopia,  as  in 
it  the  rays  returning  never  cross  or  change  their  relation  to  each 
other,  so  that  those  above  become  below  or  vice  versa^  because  the 
light  leaves  the  hyperopic  eye  in  diverging  paths.     The  observer  will 


RETINOSCOPY. 


349 


notice  that  the  movement  of  the  light  area  in  the  eye  is  always  erect, 
that  is  the  apparent  motion  is  the  same  as  the  real  motion  of  the 
light,  at  all  distances  from  the  eye.  If  the  observer  moves  backward 
and  forward,  keeping  the  light  in  the  eye  as  he  rotates  his  mirror,  he 
will  notice  that  the  movement  of  the  light  is  ever  with  the  rotation  of 
the  mirror.     This  occurs  in  emmetropia  and  hyperopia. 

With  the  ophthalmoscopic  mirror  alone  at  a  distance  of  several  feet 
from  the  eye,  a  view  of  the  fundus  is  obtained  in  an  erect  image,  so 


Original 
/^^  Source  of  Light 


by  retinoscopy  when  the  light  in  the  eye  really  moves  down,  up  or 
how  not,  its  apparent  motion  is  the  same  as  the  real  motion  because 
the  observer  is  getting  an  upright  image  of  the  fundus. 

In  myopia  the  same  rule  as  to  the  part  of  the  fundus  of  the  eye 
illumined  holds,  that  is  the  real  movement  of  light  in  the  eye  is  with 
the  rotation  of  the  mirror.  The  apparent  movement  is  not  the  same 
at  all  distances  from  the  eye  however  as  in  emmetropia  and  hyperopia. 
The  rays  of  light  emerging  from  the  myopic  eyeball  converge,  and 
crossing  in  front  of  the  eye  at  the  point  of  reversal  they  change  their 


350 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


'/ 


relation  to  each  other,  so  that  those  that  come  from  above  enter  the 
eye  of  the  observer  below  and  those  that  came  from  below,  enter  the 
eye  of  the  observer  above,   giving  him  the  impression  that  they 
^  originated  above  in  the  eye  under  observation. 

When  the  apparent  movement  of  the  light  in  the 
eye  is  opposite  to  the  real  movement  it  is  said  to 
/\  \  '•  I  \  ^^  ^^  inverted  movement.  In  myopia  so  long 
/  \  \  '/  I  as  the  observer  is  nearer  the  eye  than  the  point 
at  which  the  emitted  rays  cross,  the  apparent  and 
the  real  movement  of  light  are  the  same  (with 
the  mirror),  but  when  the  point  of  crossing  (far- 
point  of  eye)  is  nearer  the  eye  than  the  observer, 
the  motion  of  light  in  the  observed  eye  is  in- 
verted, appearing  to  move  contrary  to  the  direc- 
tion of  rotation  of  the  mirror,  that  is,  when  the 
mirror  is  turned  to  the  right  the  light  seems  to 
move  to  the  left  in  the  eye,  and  vice  versa.  The 
explanation  is  according  to  the  following  figure 
(after  Jackson). 

In  the  figure  C  and  D  are  the  external  con- 
jugates of  A  and  B,  areas  in  the  fundus  of  the 
eye.     A^  is  a  point  nearer  the  eyeball  than  these 
reversal  points  and  N'  one  further  away.     If  the 
eye  of  the  observer  is  at  N,  the  light  that  comes 
to  it  from  point  B  in  the  lower  portion  of  the  ob- 
served eyeball  is  that  which  passes  out  of  the 
pupil  of  the  observed  eye  below  and  is  turned  up. 
The  observer  places  the  point  B  in  its  true  posi- 
tion, not  taking  into  account  the  refraction  of  the 
light  as  it  passes  from  the  observed  eye  to  his  own, 
he  projects  the  point  B  as  lying  along  a  straight 
line  at  point  b.     He  then  sees  what  is  below,  as  below.     The  light 
that  comes  to  his  eye  from  the  point  A  is  thought  to  lie  along  the  line 
Na  ;  A  that  is  above  is  then  seen  above.     If  the  observer  now  moves 


RETINOSCOPY.  251 

to  the  point  N'  beyond  the  points  of  reversal,  the  conditions  have 
changed.  The  ray  that  comes  to  his  eye  now  from  A  above  is  the 
one  that  passes  through  the  lower  part  of  the  pupil  of  the  observed 
eye  and  is  bent  up ;  ^  is  then  supposed  to  lie  along  a  straight  line  at 
a',  that  is  while  A  is  really  above  it  appears  to  be  below.  During 
the  test  then  when  the  light  in  the  eye  moves  up  it  appears  to  move 
down.  By  this  fact  one  knows  that  the  point  of  reversal  lies  between 
him  and  the  patient,  or  as  we  say  the  movement  has  become  reversed. 
In  myopia  there  is  formed  at  the  far-point  of  the  eyeball  an  inverted 
real  image  of  the  fundus,  which  can  be  seen  by  the  observer.  As  it 
is  inverted  so  the  movement  of  light  in  the  eye  during  retinoscopy 
appears  inverted  seeming  to  be  below  when  really  above  and  vice 
versa.  (In  retinoscopy  we  do  not  view  the  image  of  the  fundus,  but 
movement  upon  the  fundus.) 

The  rapidity  with  which  the  light  appears  to  move  across  the  pupil 
in  retinoscopy  depends  upon  the  rapidity  of  movement  of  the  light 
area  upon  the  retina  and  upon  the  magnification  of  the  latter.  The 
rapidity  of  the  real  movement  of  the  light  upon  the  retina  depends 
upon  the  rate  of  movement  of  the  mirror  and  the  distance  of  the 
mirror  from  the  eye  under  examination,  upon  the  distance  of  the 
original  source  of  light  from  the  mirror  and  upon  the  distance  of  the 
retina  from  the  nodal  point  of  the  eye.  The  rate  of  movement  of 
the  mirror  and  the  distance  of  the  original  source  of  light  from  the 
mirror  determine  the  rate  of  movement  of  the  immediate  source  of 
light,  being  quicker  the  faster  the  mirror  is  rotated  and  the  nearer 
the  original  source  of  light  to  the  mirror.  The  excursion  that  the 
immediate  source  of  light  makes  is  limited  by  the  width  of  the  mirror, 
and  the  extent  of  the  movement  of  the  immediate  source  of  light 
upon  the  retina  depends  upon  the  relative  distances  of  the  mirror 
and  the  retina  from  the  nodal  point  of  the  eye  under  test. 

On  account  of  the  relative  distances  of  the  retina  from  the  nodal 
point  the  extent  of  the  movement  of  light  upon  the  retina,  other 
things  being  equal,  is  least  in  highest  hyperopia  and  greatest  in 
highest  myopia.     Practically  the  rate  of  movement  of  the  light  area 


352  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

on  the  retina  depends  more  upon  the  extent  to  which  the  real  move- 
ment of  light  is  magnified  than  to  the  actual  rate  of  the  real  move- 
ment. The  retina  as  it  is  viewed  from  different  distances  is  seen 
under  different  degrees  of  magnification.  When  the  eye  of  the  ob- 
server is  at  the  point  of  reversal  all  the  rays  from  a  single  point  in 
the  fundus  converge  to  the  nodal  point  of  the  observer's  eye,  so  that 
every  point  of  illumination  upon  the  retina  appears  to  occupy  the 
whole  pupillary  area.  The  retinal  illumination  therefore  is  indefi- 
nitely magnified. 

It  is  disputed  by  some  that  the  apparent  rate  of  movement  upon 
the  retina  depends  upon  the  magnification  of  the  movement  when 
close  to  the  point  of  reversal.  They  say  that  the  apparent  enlarge- 
ment of  the  reflex  is  due  to  the  increased  diffusion  upon  the  retina  of 
the  observer  and  not  upon  that  of  the  observed,  such  diffusion  reach- 
ing its  maximum  when  the  light  from  the  observed  eye  comes  to  a 
focus  just  posterior  to  the  cornea  of  the  observer's  eye,  and  the  rate 
of  movement  depends  upon  the  nearness  of  the  reversal  point  to  the 
eye  of  the  observer.  That  the  explanation  of  magnification  accounts 
for  both  the  diffusion  and  quick  movement  at  the  reversal  point  is 
proven  by  study  with  a  convex  lens  and  dot  upon  a  card,  as  pointed 
out  in  the  following  pages.  Diffusion  upon  the' retina  of  the  ob- 
server's eye  renders  the  image  of  the  light  indistinct  proportionately 
throughout  the  test,  as  can  be  demonstrated  by  rendering  oneself 
artificially  myopic  with  a  convex  lens  placed  back  of  the  sight-hole 
of  the  retinoscope,  but  does  not  make  the  movement  of  light  one  bit 
quicker.  The  pupil  of  the  observed  eye  and  the  area  of  retinal 
illumination  appear  enlarged  through  the  convex  lens,  but  they  bear 
the  same  relation  in  size  to  each  other  as  they  do  without  the  convex 
lens. 

The  nearness  of  the  point  of  reversal  to  the  nodal  point  of  the 
observer's  eye  is  however  pardy  the  cause  of  the  increased  rapidity 
of  motion  in  the  observed  eye,  as  the  point  of  reversal  is  reached. 
A  near  object  moving  with  the  same  speed  as  a  distant  one  appears 
to  cross  the  field  more  rapidly. 


RETINOSCOPY. 


353 


As  the  eye  of  the  observer  departs  from  the  point  of  reversal,  it 
receives  rays  of  Hght  from  an  increasing  area  of  retina,  and  the  retina 
is  therefore  seen  less  magnified.     See  figure  from  Jackson. 

A  is  supposed  to  be  the  point  of  reversal  of  the  eyeball  M.  At  A 
the  observer  receives  all  the  light  from  the  point  a,  and  this  point 
therefore  appears  to  occupy  the  entire  pupil.  If  however  the  ob- 
server places  his  eye  at  the  point  B  from  which  rays  would  be 
focused  at  b  behind  the  retina,  he  will  see  in  the  pupil  all  the  retina 
included  between  the  points  ni  and  n,  the  extent  of  the  circle  of  dif- 


a-r-=-b 


fusion  if  the  light  emanated  at  B.  Or  if  the  observer's  eye  was 
placed  at  the  point  C  from  which  rays  would  be  focused  at  c,  he  will 
be  able  to  perceive  the  portion  of  retina  included  between  the  broken 
lines,  the  area  upon  which  would  be  formed  a  circle  of  diffusion  if  the 
light  emanated  from  the  point  C.  It  follows  then  that  the  nearer  the 
observer's  eye  is  to  the  point  of  reversal  the  more  the  retina  and  the 
real  movement  of  light  upon  it  are  magnified,  and  that  in  consequence 
the  swifter  the  apparent  movement  across  the  pupil.  Hence  the  rate 
of  the  apparent  niove77ient  of  light  in  the  pupil  is  quicker  the  nearer 
one  is  to  the  point  of  reversal. 

The  Form  of  the  Retinal  Light  Area.  —  The  real  form  of  the  light 
area  on  the  retina  except  in  certain  conditions  in  astigmatic  eyes  is  a 
more  or  less  blurred  retinal  image  of  the  original  source  of  light, 
partaking  of  its  form,  with  either  a  plane  or  a  concave  mirror.  The 
reflection  from  a  circular  plane  mirror  when  thrown  upon  a  screen  is 
seen  to  be  circular,  no  matter  what  is  the  shape  of  the  original  source 
of  light.     The  same  is  true  of  a  concave  mirror  unless  the  screen  is 


354 


THE   EYE,    ITS    REFRACTION   AND    DISEASES. 


placed  at  the  focus  of  the  latter,  then  an  inverted  image  of  the  orig- 
inal source  of  light  is  formed  upon  the  screen.  But  after  the  re- 
flected rays  from  either  mirror  pass  through  the  dioptric  system  of 
the  eyeball  there  is  formed  a  more  or  less  blurred  image  of  the  orig- 
inal source  of  light  upon  the  fundus  of  the  eyeball.  When  a  circular 
opening  is  used  for  the  source  of  light,  the  area  of  retinal  illumination 


Form  of  Light  Area  Near  the 
Point  of  Reversal. 


Form  of  Light  Area  in  High 
Ametropia. 


is  circular.  When  the  immediate  source  of  light  (catoptric  image 
from  the  mirror)  occupies  the  point  of  reversal,  the  external  conjugate 
focus  of  the  retina,  the  focusing  is  most  accurate  and  the  area  of 
illumination  small,  circular  and  well  defined,  but  as  the  immediate 
source  departs  from  this  point,  the  focusing  becomes  more  and  more 
diffused  the  higher  the  ametropia,  and  the  edge  of  the  light  area 
approaches  a  straight  line,  due  to  the  overlapping  of  diffusion  areas 
of  the  shape  of  the  pupil  of  the  observed  eye  but  its  edge  never 
becomes  straight  save  in  cases  of  astigmatism.  In  no  case  does  the 
observer  see  a  distinct  image — for  his  eye  is  focused  for  the  pupillary 
plane  of  the  observed  eye,  while  the  image  that  he  observes  in 
myopia  is  in  front  of,  and  in  hyperopia  behind  this  plane.  The  image 
is  therefore  seen  vaguely,  each  point  in  it  being  represented  by  a 
diffusion  circle,  which  as  always  corresponds  to  the  pupil  of  the  ob- 
server.    The  theory  as  outlined  is  that  of  Parent. 

The  explanation  given  to  retinoscopy  by  Leroy,  which  is  widely 
accepted  throughout  Germany,  is  in  agreement  with  that  of  Parent. 
The  illuminated  area  upon  the  retina  is  bordered  by  a  shadow,  upon 
which  many  place  their  attention  during  the  performance  of  retinos- 


RETINOSCOPY. 


355 


copy.  This  shadow  is  caused  by  no  light  entering  the  eye  of  the 
observer  from  that  portion  of  the  pupil  of  the  observed  eye,  or  in 
other  words  the  iris  of  the  observer  as  Leroy  suggests  produces  the 
shadow.     See  the  figure  below. 

X  represents  an  illuminated  area  of  the  retina,  from  which  starts 
a  luminous  cone.     As  the  eye  is  supposed  to  be  myopic,  or  rendered 


Observed  Observer 


SO  by  a  convex  sphere,  the  light  from  x  converges  to  point  y.  The 
observer  sees  luminous  only  that  part  of  the  pupil  which  sends  rays 
to  it.  The  lower  part  of  the  observed  pupil  therefore  appears  unil- 
lumined  as  the  light  passing  through  it  is  intercepted  by  the  iris  of 
the  observer.  The  curved  form,  of  the  border  of  the  illumination  in 
the  observed  eye  is  not  explained,  however,  by  the  form  of  the  pupil 
of  the  observer.  The  form  of  the  pupil  of  the  observer  plays  no 
part,  as  the  phenomena  do  not  change  if  the  observer  looks  through 
a  stenopaic  slit  or  a  triangular  aperture  placed  in  front  of  his  pupil. 
The  form  of  each  diffusion  circle  of  the  light  area,  shaped  by  the  iris 
of  the  observer,  has  no  influence  upon  the  form  of  the  border  of  the 
light  area  upon  the  retina  of  the  observed  eye,  the  distinctness  of  its 
image  only  being  altered. 

The  brilliancy  of  the  light  in  the  pupil  depends  upon  the  bright- 
ness of  the  original  source  of  light,  and  upon  the  extent  to  which 
the  retina  is  magnified.  The  more  nearly  the  light  is  focused  upon 
the  retina  the  brighter  the  illumination  in  the  pupil.  The  luminosity 
is  diminished  as  the  point  of  reversal  is  reached  by  the  increasing 
magnification  of  the  retina,  which  causes  the  light  from  a  smaller 
part  of  the  retina  to  occupy  the  whole  pupil.  The  brightest  reflex 
is  obtained  not  at  the  point  of  reversal  but  about  i  D.  therefrom. 


35^ 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


Practical  Application  of  the  Test.  —  The  eye  to  be  tested  must 
have  its  accommodation  at  rest  and  pupil  dilated  by  a  cycloplegic, 
and  the  room  made  very  dark.  The  light  should  be  back  of  the 
patient,  at  the  height  of  his  eye  and  on  the  same  side  of  his  head  as 
the  eye  to  be  tested.  The  opening  in  the  shade  that  screens  the 
light  should  be  large  at  first  and  made  smaller  as  one  approaches  the 

point  of  reversal ;  the  mir- 
ror also  should  be  small 
when  near  the  reversal 
point.  The  ordinary  trial 
frame  and  test  case  may  be 
used  for  retinoscopy,  but  it 
is  much  more  convenient 
and  conducive  to  good  work 
to  be  provided  with  some 
sort  of  a  refractometer,  by 
which  one  is  enabled  to  re- 
volve before  the  eye  lenses 
in  quick  succession  without 
leaving  one's  position.  To 
leave  your  seat  every  time 
a  change  in  the  lens  before 
the  eye  is  needed  is  tire- 
some and  takes  time.  The 
refractometer  of  Lambert 
is  as  good  if  not  better  than 
any  on  the  market.  The 
Cross  retinoskiameter,  and 
the  Meyrowitz  improved  re- 
fractometer are  among  the  best.  Many  use  the  hand  skiascope — the 
patient  holds  the  slide  in  front  of  the  eye  and  moves  it  up  or  down  as 
the  examiner  dictates.  It  is  hardly  ever  held  properly  and  not  nearly 
as  convenient  as  an  instrument  that  can  be  operated  by  the  observer. 
The  Lambert  instrument  consists  of  two  superimposed  metal  discs, 


Gruenig's  Set  of  Hand  Skiascopes. 


RETINOSCOPY. 


357 


eleven  inches  in  diameter,  one  of  which  contains  nine  convex  lenses 
ranging  from  +  i  D.  to  +  9  D.,  and  ten  concave  lenses  from  -  i  D.  to 
—  10  D.,  while  the  other  carries  both  the  convex  and  concave  fractional 
and   10  D.  lenses.     On  the  reverse  side  of  the  instrument  is  an  arm, 


carrying  an  eye-piece,  which  can  be  swung  to  either  side  of  the  disc, 
according  to  which  eye  is  to  be  tested.  Attached  to  this  arm  is  a 
gfraduated  cell  in  which  the  cylindrical  trial  lenses  can  be  placed  at 


358 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


any  desired  angle.  The  combination  of  all  foci  is  obtained  in  the 
same  manner  as  in  the  Loring  ophthalmoscope,  and  the  graduated 
cell  permits  the  rotation  of  the  cylinders  to  all  axes.  The  lenses  are 
one  and  one  half  inches  in  diameter,  and  the  instrument  can  be  used 
for  refraction  work  as  well  as  retinoscopy.  Attached  to  the  eye-piece 
is  an  extra  cell  which  will  hold  either  a  solid  disc  to  cover  the  other 
eye  in  retinoscopy  or  a  trial  lens  in  testing  both  eyes  for  refraction. 
Both  discs  can  be  revolved  either  independently  or  together,  with 


MIXED 

AS. 

H.  PREDOMINATING 


*l.  AS.  M.  PREDOMINATING^ 


/if^ 


IRREG.  AS. 
H.  PREDOMINATING 


IRREG.  AS.  M.  PREDOMINATING 


Appearances  of  Source  of  Light  with  Ridgeway's  Glass. 

one  hand,  at  the  will  of  the  operator,  when  at  a  distance  of  one  meter 
from  the  patient,  by  means  of  a  gear  movement  operated  by  a  rod 
and  hollow  tube.  The  rod,  which  turns  within  the  hollow  tube, 
operates  the  main  disc ;  the  auxiliary  disc  is  rotated  by  means  of  the 
tube.  A  quarter  turn  brings  a  lens,  by  consecutive  increase  or  de- 
crease, before  the  eye-piece. 

The  elbow  joint,  which  supports  the  lens  discs,  rotates  on  the  up- 


RETINOSCOPY. 


359 


right  standard  in  such  a  manner  that  the  lenses  can  be  placed  before 
either  eye  of  the  patient  without  any  change  of  position. 

The  figures  are  in  large  black  and  white  letters,  and  can  readily  be 
seen  in  the  dark-room. 

The  Meyrowitz  refractometer,  one  of  the  newer  instruments  upon 
the  market,  consists  of  a  highly  polished  base  to  which  are  fixed  two 
uprights  which  carry  a  number  of  discs,  each  disc  containing  twenty- 
one  lenses,  ranging  from  0.25  D.  to  7  D.  in  both  positive  and  minus 
lenses.     In  making  the  test  the  chin  of  the  patient  rests  in  an  ad 


The  Cross  Retinoskiameter. 


justable  chin-piece  which  is  raised  or  lowered  by  a  milled  head,  while 
the  forehead  is  placed  against  the  head-rest  which  connects  the  two 
uprights  holding  the  discs.  The  pupillary  distance  is  obtained  by 
moving  the  two  discs  in  a  lateral  position. 

The  discs  are  rotated  by  two  rods  having  milled  heads,  the  length 
of  these  rods  gives  the  required  distance  of  one  meter  between  the 
lens  discs  and  the  eye  of  the  operator.  The  objection  to  all  instru- 
ments of  this  kind  is  that  the  lenses  are  at  too  great  a  distance  from 
the  eyes  of  the  patient. 


360 


THE   EYE,    ITS    REFRACTION    AND    DISEASES. 


The  mechanism  is  so  arranged  that  a  distinct  click  is  noticed  as 
each  lens  comes  before  the  eye,  and  the  lenses  are  changed  with 
rapidity  without  disturbing  the  patient  in  any  way. 

Two  of  the  discs  contain  plus  lenses,  and  two  contain  minus  lenses, 
the  disc  not  in  use  being  accommodated  in  two  drawers  in  the  base 
of  the  instrument. 

The  Cross  retinoskiameter  consists  of  two  7  D.  convex  and  two 
7  D.  concave  cylindrical  lenses  mounted  in  cells,  with  their  axes  at 
right  angles  to  each  other,  each  lens  being  inclined  slightly  on  its 
axis  from  the  perpendicular.  The  two  concave  lenses  are  stationary, 
while  the  two  convex  ones  are  movable,  their  cells  sliding  on  rods 
and  being  controlled  by  a  double  cord  forty  inches  in  length.  The 
pointers  on  the  side  of  each  tube  show  the  kind  and  the  focal 
strength  of  the  lenses.     The  tubes  revolve,  changing  the  axes  of  the 

cylinders.  The  cells  are  operated 
either  backward  or  forward  by  a 
simple  devise.  By  the  construc- 
tion of  the  instrument  the  pupil  of 
the  observed  eye  is  magnified  sev- 
eral times,  thus  facilitating  the  test. 
A  point  about  the  instrument  upon 
which  stress  is  laid  is  that  the  lens 
strength  before  the  eye  is  changed 
gradually  and  not  by  jumps  as  we  do  usually  when  we  replace  a  .25 
by  a  .50  D.  lens  and  so  on,  thus  causing  more  acccommodation  to 
be  relaxed,  but  as  it  is  necessary  to  use  a  mydriatic  in  retinoscopy, 
as  in  other  methods  of  testing  refraction  to  be  sure  that  the  eyes  are 
at  rest,  this  is  of  no  especial  importance,  unless  one  wishes  to  test 
without  the  aid  of  a  cycloplegic. 

The  Lambert  refractometer  is  to  be  preferred.  The  instrument  is 
placed  before  the  patient  with  the  eye  to  be  tested  behind  the  sight- 
hole,  and  the  other  eye  protected  by  a  shield  held  in  a  clip  attached 
to  the  eye-piece.  The  handle  of  the  instrument,  which  is  detachable, 
is  put  in  place.     The  examiner  takes  a  position  of  one  meter  or 


RETINOSCOPY.  36 1 

slightly  more  from  the  patient,  and  reflects  the  light  into  the  eye. 
He  then  sees  the  pupil  filled  with  a  red  glare,  and  on  rotating  the 
mirror  a  movement  in  this  light  area  is  noticed.  Some  advise  that  the 
attention  be  placed  upon  the  edge  of  the  light  or  bordering  shadow, 
but  it  is  much  easier  to  watch  the  movement  of  the  light  itself  The 
retinoscope  is  supported  by  resting  the  edge  of  the  mirror  against 
the  side  of  the  nose,  and  the  handle  of  the  instrument  is  held  hori- 
zontally. Rotation  can  then  be  performed  in  any  meridian  with  the 
greatest  ease.  On  rotating  the  mirror  from  side  to  side  the  observer 
will  note  that  the  light  in  the  eye  moves  in  the  same  meridian  unless 
oblique  astigmatism  is  present.  In  astigmatism  if  rotation  of  the 
mirror  takes  place  in  a  meridian  forming  an  angle  with  one  of  the 
principal  meridians  of  the  eye,  the  light  area  in  the  eye  moves  in  a 
meridian  oblique  to  that  in  which  the  mirror  is  rotated. 

This  oblique  movement  is  more  decided  in  the  higher  forms  of 
astigmatism,  and  therefore  in  mixed  astigmatism  as  a  rule.  If  the 
principal  meridians  are  1 5  degrees  or  so  from  the  vertical  and  hori- 
zontal the  light  will  be  seen  to  move  vertically  when  the  mirror  is 
turned  from  side  to  side,  and  obliquely  from  above  downwards  — 
from  the  upper  nasal  quadrant  to  the  lower  temporal,  or  upper  tem- 
poral to  lower  nasal  or  vice  versa,  if  the  principal  meridians  are  in 
the  neighborhood  of  45  and  135  degrees. 

If  the  light  moves  in  the  same  meridian  in  the  eye  as  it  does  upon 
the  face  of  the  patient,  there  is  no  astigmatism  present  or  the  rotation 
of  the  mirror  is  across  one  principal  meridian.  If  astigmatism  is 
present,  rotating  the  mirror  across  a  meridian  forming  an  angle  with 
that  of  the  primary  rotation,  will  cause  the  light  in  the  eye  to  move 
obliquely.  Unless  the  error  is  over  .50  D.,  this  oblique  movement  can 
not  be  detected.  If  the  light  in  the  eye  appears  to  move  in  the  same 
direction  as  that  in  which  the  mirror  is  rotated,  the  observer  moves 
further  back,  and  if  the  movement  continues  erect,  there  is  present 
either  emmetropia  or  hyperopia  in  that  meridian,  but  myopia  exists, 
if  as  he  recedes  from  the  eye  the  movement  becomes  very  indistinct 
and  then  inverted,  that  is  against  the  rotation  of  the  mirror  or  the 


362  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

light  Upon  the  face  of  the  patient.  If  the  movement  of  the  Hght  in 
the  observed  eye  is  erect  at  all  distances  one  differentiates  between 
emmetropia  and  hyperopia  in  the  following-  manner :  Seated  at  a 
distance  of  i  m.,  the  observer  rotates  before  the  eye  a  i  D.  S. 
lens,  which  if  there  is  emmetropia  present  will  impart  to  the  eye 
I  D.  of  myopia,  and  as  the  far  point  of  the  eye  would  then  be  an- 
terior to  the  eye  of  the  observer,  the  movement  of  the  light  in  the 
pupil  would  now  be  inverted,  that  is  against  the  rotation  of  the 
mirror,  or  in  a  direction  opposite  to  the  movement  of  the  light  upon 
the  face  of  the  patient.  The  observer  now  rotates  the  mirror  in  dif- 
ferent directions,  and  if  the  movement  of  the  light  in  the  eye  is 
always  parallel  to  the  axis  of  rotation  of  the  mirror,  the  shape  of  the 
light  always  circular,  inverted  in  all  meridians,  and  not  inverted  by  a 
weaker  lens  in  any  meridian,  the  test  is  concluded  with  emmetropia 
as  the  diagnosis. 

In  a  case  of  hyperopia  the  movement  of  light  and  shade  in  the 
pupil  is  seen  to  be  with  the  mirror,  and  it  continues  to  be  so  with  a 
plus  one  diopter  lens  before  the  eye.  Suppose  that  the  present  case 
is  one  of  3  D.  of  hyperopia.  The  movement  of  light  will  continue 
erect  as  successive  strengths  of  lenses  are  added  until  a  plus  4  D. 
S.  is  reached,  when  the  movement  becomes  inverted,  being  now 
against  the  rotation  of  the  mirror,  moving  to  the  right  when  the  mirror 
was  turned  to  the  left  and  so  on.  The  eye  is  rendered  myopic  by 
the  plus  4  D.  S.  lens  and  the  point  of  reversal  is  brought  to  lie 
just  in  front  of  the  eye  of  the  observer.  If  it  takes  a  plus  4  D.  lens 
to  make  an  eye  one  diopter  myopic  there  must  have  been  3  D.  of 
original  hyperopia  (4—1  =3  D.). 

Suppose  that  it  takes  only  a  +  .50  D.  lens  to  reverse  the  movement 
of  light  in  the  eye,  what  is  the  error  ?  Inasmuch  as  it  takes  a  plus 
lens  to  reverse  the  movement  we  subtract  i  D.  from  the  strength  of 
the  lens  before  the  eye  when  the  movement  has  become  reversed,  to 
obtain  the  original  refraction  of  the  eye,  which  would  be  +.50  D.  — 
•I  =  —  .50  D.  or  .50  D.  of  myopia.  If  the  eye  under  test  has  over 
one  diopter  of  myopia  the  movement  of  the  light  will  be  found  in- 


RETINOSCOPY.  363 

verted  without  any  lens  before  the  eye  at  the  distance  of  one  meter 
and  twenty  centimeters,  as  the  observer  seated  at  that  distance  would 
be  behind  the  point  of  reversal  for  i  D.  of  myopia.  Myopia  less 
than  I  D.  is  detected  as  above,  or  as  the  observer  moves  further  from 
the  eye,  the  movement  will  become  inverted  just  as  soon  as  he  passes 
beyond  the  far-point  of  the  eye. 

If  when  beginning  the  test  in  myopia  the  light  in  the  eye  is  seen 
to  move  against  the  mirror,  at  the  usual  distance  of  i  meter 
minus  spherical  lenses  are  added  in  increasing  strengths  until  the 
weakest  one  is  found  that  causes  the  movement  of  light  to  be 
erect,  that  is  causes  the  light  to  move  with  the  rotation  of  the  mirror 
as  it  does  in  hyperopia  and  in  emmetropia.  There  still  remains  i  D. 
of  myopia  after  the  reversal  of  light  occurs,  the  lens  before  the  eye 
under  the  test  only  partially  correcting  its  error.  Then,  in  an  eye, 
if  it  takes  a  —  2  D.  lens  to  correct  all  of  the  myopia  save  i  D.  there 
must  originally  have  existed  3  D.  of  myopia.  So  to  obtain  the 
amount  of  myopia  we  add  one  to  the  lens  that  is  needed  to  reverse 
the  movement  of  light  in  the  eye,  or  to  have  the  same  rule  apply  as 
in  hyperopia  we  say  that  we  subtract  —  i  D.  from  the  lens  of  reversal, 
which  is  the  same  thing  as  adding  one  (2  —  (  —  i)  =  3  D.). 

Take  for  example  a  myopia  of  6  D.  At  first  glance  the  light 
moves  against  the  rotation  of  the  mirror  as  it  does  when  —  i,  —2, 
—  3  and  —  4  D.  S.  lenses  are  placed  before  the  eye.  When  a  —  5  D. 
is  placed  before  the  eye  the  movement  becomes  erect,  as  the  far- 
point  of  the  eye  or  the  point  of  reversal  has  been  brought  to  lie  pos- 
terior to  the  observer's  nodal  point.  The  same  lens  causes  the 
movement  in  all  meridians  to  be  erect,  unless  astigmatism  is  present. 

Instead  of  the  observer  taking  his  position  before  the  observed  eye 
and  adding  lenses  until  the  point  of  reversal  has  been  brought  to  his 
eye,  he  may  change  the  lenses  less  often  and  move  backwards  and 
forwards  until  he  finds  the  place  where  the  direction  of  the  move- 
ment of  light  changes,  marking  the  location  of  the  point  of  reversal. 
The  distance  of  this  point  in  cm.  divided  into  100  cm.  will  give  the 
amount  of  myopia.     Thus,  suppose  that  the  movement  of  light  is 


254  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

erect  nearer  to  an  eye  than  50  cm.  and  further  from  the  eye  than 
this  point,  inverted.  The  reversal  then  takes  place  in  the  vicinity 
of  50  cm.  from  the  observed  eye.  This  error  is  equal  to  2  D.  of 
myopia  (100-^50=2  D.).  If  the  error  is  high,  shown  by  the  poor 
illumination  in  the  pupil  of  the  observed  eye  and  by  the  slow  move- 
ment of  the  light,  as  the  mirror  is  rotated,  a  minus  lens  of  ap- 
proximate strength  is  placed  before  the  eye,  so  as  to  remove  the 
point  of  reversal  further  off,  in  order  that  its  position  may  be  more 
accurately  determined. 

The  far-point  of  10  D.  of  myopia  lies  anterior  to  the  eye  10  cm, 
(100/10=  10)  and  that  of  9  D.,  11  cm.  anterior  to  the  eye,  a  centi- 
meter only  separating  the  far-points  of  errors  differing  by  a  diopter, 
but  let  each  case  be  nearly  corrected,  then  the  distance  between  the 
far-points  increases.  Suppose  that  the  amount  uncorrected  equals  a 
.50  D.  in  one  instance  and  1.50  D.  of  myopia  in  another,  then  the  far- 
points  lie  at  2  m.  and  66  cm.  respectively.  To  accurately  ascertain 
the  distance  of  the  point  of  reversal  from  the  observed  eye,  the 
patient  holds  one  end  of  a  centimeter  tape  line  at  the  outer  angle  of 
the  eye,  the  observer  holding  the  other  end  in  the  hand  that  holds 
the  retinoscope.  If  the  end  of  the  line  is  weighted,  it  will  not  be 
necessary  to  take  up  any  slack  as  the  observer  approaches  the  patient 
if  the  tape  is  held  loosely  in  the  hand.  The  furthest  point  at  which 
the  erect  movement  is  seen  is  noted,  and  the  nearest  point  at  which 
the  inverted  movement  is  perceived  is  noted.  The  distance  between 
these  points  is  halved  and  the  amount  added  to  the  greatest  distance 
at  which  the  erect  movement  was  observed,  and  divided  into  100  cm. 

In  hyperopia,  instead  of  gradually  changing  the  strength  of  the 
lens  until  the  point  of  reversal  is  reached,  one  may  by  trial  obtain  a 
lens  that  over-corrects  the  case,  leaving  it  myopic.  The  amount  of 
myopia  is  then  measured  by  finding  the  position  of  the  far-point  after 
the  manner  described.  The  amount  of  myopia  is  then  subtracted 
from  the  lens  before  the  eye,  to  obtain  the  amount  of  original  hyper- 
opia. Thus,  suppose  that  we  have  a  case  of  4  D.  H.  A  +  6  D.  lens 
is  placed  before  the  eye  by  guess,  the  movement  of  light  in  the  eye 


RETINOSCOPY.  365 

is  seen  to  be  inverted  at  about  a  meter's  distance.  The  observer 
then  moves  backward  and  forward  as  he  rotates  his  mirror  and  at 
about  50  cm.  from  the  eye  he  notices  that  the  movement  of  the  Hght 
changes.  The  amount  of  myopia  then  equals  2  D.  (100/50  =  2  D.). 
6  D.  (lens  before  the  eye)  —2D.  (amount  of  myopia  produced)  = 
4  D.  (amount  of  original  hyperopia). 

The  method  of  maintaining  one's  position  and  adding  lenses  to  the 
eye  to  bring  the  point  of  reversal  to  one  meter's  distance  is  rather 
more  accurate  than  the  method  of  changing  one's  position  in  search 
of  the  point  of  reversal.  By  retinoscopy  it  is  possible  to  measure 
.12  D.  of  error  but  much  practice  is  necessary  to  do  that  well,  es- 
pecially in  astigmatism.  Whenever  there  is  any  doubt  as  to  which 
lens  reverses  the  movement,  select  the  weaker  and  then  there  is  no 
danger  of  over-correction. 

The  astigmatic  eye,  myopic  or  rendered  so  by  the  addition  of  a 
positive  spherical  lens,  has  many  points  of  reversal,  but  we  are  alone 
concerned  with  the  points  of  reversal  of  the  principal  meridians. 
There  are  then  two  practical  points  of  reversal  in  the  astigmatic  eye. 
The  figure  below  shows  a  myopic  astigmatic  eye,  with  the  two  points 
of  reversal,  one  for  each  principal  meridian. 

M  is  the  far-point  of  the  eye  through  the  meridian  m,  and  N  the 
far-point  through  the  me-  ^^  ^  ^^ 

ridian  n.  If  the  eye  of 
the  observer  is  nearer 
one  far-point  than  the  y^'^-^zsZSI^ 
other,  the  retina  is  seen 
more  magnified  in  the 
meridian  of  that  far-point, 
each  point  of  illumination  upon  the  retina  appearing  to  occupy  the 
whole  pupillary  area.  This  with  the  unequal  focusing  of  the  light 
upon  the  retina  in  the  two  principal  meridians  of  the  eye  causes  the 
light  to  be  drawn  out  into  a  band  or  ribbon  running  across  the  pupil, 
bounded  by  the  linear  shadow  of  Bowman. 

As  taught  by  Jackson  and  others,  the  band  appearance  is  most 


366  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

distinct  when  the  eye  of  the  observer  is  at  the  point  of  reversal  for 
one  principal  meridian  and  the  immediate  source  of  light  at  the  point 
of  reversal  for  the  other  meridian.  By  reference  to  the  figure 
above  it  will  be  seen  that  when  the  eye  of  the  observer  is  at 
point  N,  the  retina  will  be  most  magnified  in  meridian  71,  caus- 
ing each  point  of  light  upon  the  retina  to  occupy  the  whole  pupil, 
causing  the  illumination  to  appear  in  the  form  of  a  band  in  the  ver- 
tical meridian.  If  the  source  of  light  is  at  Af  the  conjugate  of  the 
retina  in  the  horizontal  meridian,  the  focusing  of  the  light  crosswise 
through  the  meridian  m  will  be  accurate,  adding  to  the  distinctness 
of  the  band.  Then,  with  a  plane  mirror,  after  the  strongest  lens  has 
been  found  that  reverses  the  movement  of  light  in  all  meridians  of 
the  eye,  the  observer  moves  closer  to  the  eye  until  he  finds  the  point 
of  reversal  for  the  most  myopic  meridian  (with  lens  on)  by  noting 
the  place  where  the  movement  becomes  erect  for  that  meridian.  His 
eye  is  now  at  one  point  of  reversal,  the  other  lying  behind  him.  In- 
asmuch as  the  reflected  image  from  a  plane  mirror  always  lies  behind 
the  mirror  the  original  source  of  light  must  be  pushed  further  away 
(it  having  been  close  to  the  mirror  up  to  this  point),  so  as  to  throw 
the  immediate  source  of  light  back  to  the  point  of  reversal  of  the 
least  myopic  meridian  of  the  eyeball.  In  myopia,  after  the  lens  is 
found  that  reverses  the  movement  in  all  meridians,  the  observer  must 
move  backward  to  get  his  eye  at  the  point  of  reversal  for  the  most 

myopic  meridian.  The  band  of  light  when 
using  the  plane  mirror  then  occupies  the 
meridian  of  the  greatest  refraction  (most 
myopic). 

If  a  concave  mirror  is  used  the  observer 
locates  the  point  of  reversal  of  the  least 
myopic  meridian  and  then  draws  the  orimnal 

Band  of  Light  in  Astigmatism.  r  i-    i  i        i  •  ^V-i  • 

source  01  light  towards  the  mirror.  Ihis 
throws  the  immediate  source  of  light  nearer  the  eye,  inasmuch  as  the 
catoptric  image  from  the  concave  mirror  lies  in  front  of  the  mirror. 
The  band  is  then  best  defined  the  moment  the  light  occupies  the 


RETINOSCOPY. 


Z^7 


point  of  reversal  of  the  meridian  of  the  greatest  refraction.  With  the 
concave  mirror  then,  the  band  occupies  the  meridian  of  the  least 
refraction.  Jackson  says  that  with  either  mirror  the  band  can  not  be 
made  to  appear  to  occupy  both  meridians,  but  in  this  he  is  mistaken. 
The  chief  factor  in  the  development  of  the  band  appearance  is  the 
fact  that  in  astigmatism  the  retina  appears  magnified  most  in  the 
meridian  that  has  its  far-point  at  the  observer's  eye. 

This  band  appearance  of  light  in  the  eye  is  characteristic  of  astig- 
matism. The  direction  of  the  band  of  light  marks  the  principal 
meridians,  if  the  strongest  or  the  Mreakest  spherical  lens  that  reverses 
the  movement  of  the  light  in  all,  or  in  any  one  direction  is  before  the 
eye.  After  the  band  appearance  is  developed  in  astigmatism  denot- 
ing the  direction  of  the  principal  meridians,  the  refraction  is  measured 
in  each  of  these  meridians  as  in  simple  hyperopia  or  myopia.  To 
ascertain  with  accuracy  the  direction  that  the  ribbon  or  the  band  of 
light  occupies  a  metallic  disc  with  a  central  opening  is  placed  before 
the  eye  (axonometer),  in  the  lens  holder.  Across  the  face  of  the 
disc  is  painted  a  broad  white  line,  bisecting  the  opening  at  its  center. 

After  the  band  is  developed,  the  disc  is  rotated  until  the  line  across 
its  face  and  the  light  band  in  the  pupil  are  continuous.  The  inclina- 
tion of  the  line  is  then  read  from  the  graduations  upon  the  trial  frame 
that  holds  the  disc.  To  get  this  appearance,  so  characteristic  of 
astigmatism,  the  source  of  light  should  be  shaded.  A  circular  open- 
ing in  the  shade  of  5  mm.  is  the  proper  size  for  nicety  of  testing, 
especially  when  working  near  the  point  of  reversal.  A  larger  open- 
ing emits  more  light,  but  then  the  observer  is  annoyed  by  the  pres- 
ence of  any  spherical  aberration  in  the  eye  under  observation. 

The  smaller  the  area  of  retina  illumined,  the  easier  is  it  to  confine 
one's  attention  to  the  movement  of  the  light  in  the  visual  zone. 
When  the  area  of  illumination  is  large  it  passes  into  the  eye  both 
through  the  center  and  the  equator  of  the  lens.  The  equator  of  the 
lens  being  weaker  or  stronger  than  the  center  causes  the  light  in  the 
pupil  to  appear  brighter  in  the  center  or  upon  the  edge  of  the  pupil, 
according  to  which  portion  has  its  point  of  reversal  nearest  to  the 


368  THE   EYE.    ITS    REFRACTION   AND    DISEASES. 

observer's  eye.  When  near  the  point  of  reversal  for  the  visual 
zone  the  light  in  the  center  of  the  pupil  and  that  in  the  periphery 
of  the  pupil  appear  to  be  separated  by  a  shadow  to  which  the  name 
of  the  paracentral  shadow  has  been  given.  Bitzos  was  the  first  to 
describe  this  shadow.  The  following  is  the  explanation  of  this 
phenomenon.  Let  it  be  supposed  that  in  an  emmetropic  eyeball  the 
peripheral  parts  of  the  pupil  are  so  refractive  that  there  is  actually 
myopia.  Rays  emanating  from  the  fundus  would  then  have  the 
direction  as  shown  in  the  cut. 

Rays  I  and  2  are  parallel  and  enter  the  observing  eye.  Rays  3 
and  4  through  the  myopic  edge  of  the  pupil  come  to  a  conjugate  focus 
at  A,  and  diverge  ;  ray  4  enters  the  observer's  pupil  while  ray  3  is 
intercepted  by  the  observer's  iris.  The  observer  therefore  sees  the 
portion  of  the  pupil  of  the  observed  eye  dark  in  place  correspond- 


Observed  Observer 

ing  to  ray  3.  This  paracentral  shadow  is  nothing  else  than  the 
manifestation  of  spherical  aberration.  To  ascertain  with  accuracy 
which  movement  of  light  belongs  to  the  visual  zone  when  near  the 
point  of  reversal  is  difficult.  Frequently  the  movement  of  light  upon 
the  edge  and  that  in  the  center  of  the  pupil  are  in  reverse  directions. 
This  annoyance  is  done  away  with  by  placing  before  the  eye  an 
opaque  screen  with  a  central  opening  the  size  of  the  undilated  pupil 
(4  mm.).  The  light  is  cut  off  from  the  periphery  of  the  pupil  by  the 
screen.  The  test  is  not  rendered  any  easier  thereby,  however,  be- 
cause it  is  more  difficult  to  tell  the  direction  of  the  movement  of  light 
when  its  excursion  is  so  small,  and  more  difficult  to  keep  the  light 
in  the  pupil,  the  excursions  of  the  mirror  being  necessarily  short. 
There  is  danger  also  of  measuring  through  the  edge  of  the  cornea  if 
the  patient  tilts  his  head. 


RETINOSCOPY. 


569 


This  phenomenon  of  spherical  aberration  is  frequently  taken  for 
the  appearance  so  often  presented  in  cases  of  irregular  mixed  astig- 
matism, what  is  termed  the  scissor  movement  of  the  light.  The 
scissor  movement  is  that  on  rotating  the  mirror,  two  areas  or  bands 
of  light  are  seen  to  approach  and  to  recede  from  each  other,  but 
never  passing,  each  area  of  light  only  moving  partly  across  the 
pupillary  space,  and  not  the  crossing  of  two  differently  moving  areas 
of  light  in  the  pupil,  as  is  seen  in  cases  of  aberration.  The  scissor 
movement  occurs  only  in  cases  of  irregular  mixed  astigmatism.  In 
compound  irregular  astigmatism  the  two  areas  or  bands  of  light 
move  together  either  with  or  against  the  rotation  of  the  mirror  as  the 
case  may  be,  but  separated  by  a  shadow.  The  typical  scissor 
movement  is  seldom  seen  except  in  cases  of  ectasia  corneae,  or  in 
subluxation  of  the  crystaUine  lens.  The  band  appearance  of  light  in 
the  observed  eye  is  often  seen  without  any  lens  before  the  eye  on  first 
throwing  the  light  into  the  eye,  especially  if  the  plane  mirror  is  used. 

In  simple  hyperopic  astigmatism  of  no  amount  is  there  to  be  seen 
at  first  a  well-defined  band  of  light  in  the  pupil.  A  slight  flattening 
of  the  circular  light  area  may  be  noticed  in  the  meridian  of  the  great- 


The  Bands  in  Compound  Ir-  Scissors    Movement  ;    Bands 

regular     Astigmatism     Moving       Separating  on  Rotating  Mirror, 
down  Together. 


The  Bands  in  Compound  Ir- 
regular Astigmatism  Moving  Up 
Together  as  Mirror  is  Rotated. 


est  refraction.  When  plus  spherical  lenses  are  added,  and  the  point 
of  reversal  of  the  previously  emmetropic  meridian  is  approximated, 
a  band  appears  running  across  the  previously  emmetropic  meridian. 
In  compound  astigmatism  of  no  degree  is  there  to  be  seen  the  band 
appearance,  until  a  plus  or  minus  sphere  is  placed  before  the  eye  that 
reverses  the  movement  in  the  least  ametropic  meridian ;  the  band  then 
24 


370  THE   EYE.    ITS   REFRACTION   AND   DISEASES. 

appears  running  across  the  meridian  of  least  ametropia.  In  mixed 
astigmatism  of  all  degrees  a  band  of  light  is  seen  running  across  the 
meridian  of  myopia.  There  is  always  a  more  apparent  movement  of 
the  light  from  side  to  side  than  from  above  downward,  as  the  excur- 
sion of  the  light  from  side  to  side  is  not  interfered  with  by  the  edges 
of  the  lids.  This  is  especially  true  in  cases  of  astigmatism  with  the 
rule,  as  it  is  more  difficult  to  discern  movement  in  the  direction  of 
the  length  of  the  band  of  light  than  it  is  at  right  angles  to  it.  To 
obviate  this  difficulty,  a  cylinder  of  the  proper  strength  to  reverse 
the  movement  at  right  angles  to  the  band  should  be  placed  before 
the  eye  with  its  axis  over  the  meridian  to  be  measured,  then  spheres 
added  until  the  point  of  reversal  is  reached  for  that  meridian. 

The  refraction  correction  of  the  eye  in  the  two  principal  meridians 
is  represented  by  the  strength  of  the  cylinder  and  the  sphere  before 
the  eye  minus  one,  respectively. 

Unless  the  astigmatic  error  is  over  .50  D.  it  is  difficult  to  develop 
a  band  of  light  in  the  pupil,  or  the  apparent  oblique  movement  of 
light  when  rotation  of  the  mirror  takes  place  in  a  meridian  other  than 
one  of  the  principal  ones.  The  astigmatism  is  then  detected  by  the 
movement  becoming  inverted  in  one  meridian  before  it  does  in  the 
others.  So  after  the  lens  is  found  that  apparentlyreverses  the  move- 
ment in  all  meridians,  the  observer  should  move  a  little  closer  and 
note  whether  the  movement  becomes  erect  in  all  directions  at  the 
same  point  and  then  moving  a  little  further  back  notice  whether  the 
movement  becomes  inverted  for  all  the  meridians  at  once. 

The  use  of  a  stenopaic  slit  opening  in  the  shade  enclosing  the 
original  source  of  light  for  retinoscopy  has  been  advocated.  The  slit 
is  placed  vertically  when  the  horizontal  meridian  of  the  eye  is  meas- 
ured and  horizontally  when  the  vertical  meridian  is  refracted,  but 
there  is  nothing  to  be  gained  by  this  method. 

In  estimating  the  error  in  the  chief  meridians,  the  rotation  of  the 
retinoscope  is  kept  parallel  with  and  at  right  angles  to  the  band  of 
light.  This  is  done  by  keeping  the  axonometer  before  the  eye  and 
causing  the  light  reflected  upon  the  face  and  into  the  eye  to  travel 


RETINOSCOPY. 


371 


along  the  painted  line  upon  the  face  of  the  disc.  After  one  meridian 
is  measured  the  disc  is  turned  so  that  the  direction  of  the  line  cor- 
responds to  the  other  principal  meridian,  which  is  measured  in  like 
manner.  We  measure  the  refraction  of  the  eye  by  retinoscopy  in 
the  meridians  of  rotation  of  the  mirror.  The  cross  meridian  is  meas- 
ured by  rotating  the  mirror  crosswise  and  vice  versa.  One  usually 
begins  the  test  by  turning  the  retinoscope  from  side  to  side  and  then 
from  above  down,  to  form  an  idea  of  the  sort  of  refraction  of  the 
eye.  It  at  times  happens  that  on  rotating  the  mirror  from  side  to 
side  the  light  in  the  eye  is  seen  to  move  in  an  oblique  direction, 
as  has  been  said.  By  changing  the  axis  of  rotation  of  the  mirror, 
while  the  light  is  kept  moving  in  the  eye,  a  meridian  is  at  last  found 
in  which  the  light  moves  in  the  eye  in  the  same  meridian  as  it  does 
upon  the  face  of  the  patient ;  the  approximate  angle  of  the  movement 
of  the  light  in  the  eye  is  then  noted  and  the  perforated  disc  placed 
before  the  eye,  and  the  band  of  light  developed  to  definitely  ascer- 
tain the  inclination  of  the  principal  meridians. 

Instead  of  using  an  axonometer  the  meridian  of  the  rotation  of  the 
mirror  may  be  fixed  by  some  device.  Such  an  appliance  has  been 
invented  by  Dr.  Fuller,  of  Chicago.  It  consists  of  an  opaque  disc 
containing  a  mirror  set  axially  in  a  ring  on  which  are  marked  degrees. 
Rotation  of  the  disc  in  the  rim  changes  the  axis  of  the  mirror  without 
altering  its  plane.  The  outer  rim  is  attached  to  a  standard  which 
can  be  fastened  to  the  edge  of  a  table,  but  it  may  be  held  in  the 
hand.  If  the  mirror  is  laid  aside  and  taken  up  again  it  will  have  the 
same  axis  of  rotation  as  before. 

The  apparent  movement  of  light  in  the  observed  eye  oblique  to 
the  movement  of  the  light  upon  the  face  of  the  patient  as  reflected 
from  the  mirror,  in  cases  of  oblique  astigmatism,  when  the  mirror  is 
rotated  from  side  to  side  or  from  above  downwards,  or  in  any  case 
of  astigmatism  when  the  rotation  of  the  mirror  is  not  across  one 
principal  meridian,  is  an  optical  illusion.  In  astigmatism  the  form  of 
the  retinal  illumination  is  in  the  form  of  an  ellipse  which,  as  it  sweeps 
across  the  retina,  gives  the  impression  that  it  is  moving  obliquely  if 


372 


THE   EYE.    ITS   REFRACTION   AND    DISEASES. 


its  motion  forms  an  angle  with  one  of  its  axes,  when  its  real  motion 
is  horizontal.  This  fact  is  demonstrable  by  drawing  an  ellipse  with 
oblique  axes  upon  a  card,  and  viewing  it  through  a  hole  in  another 
card,  while  it  is  moved  from  side  to  side.  The  ellipse  appears  to 
move  obliquely  whenever  its  motion  is  at  an  angle  to  one  of  its  axes. 
In  mixed  astigmatism  the  movement  of  the  light  is  inverted  in  one 
direction  while  it  is  erect  in  the  meridian  at  right  angles  thereto. 
This  likewise  occurs  during  the  correction  of  compound  astigmatism 
when  the  lens  before  the  eye  undercorrects  one  principal  meridian 
and  overcorrects  the  other.  In  cases  where  the  principal  meridians 
are  vertical  and  horizontal  there  is  no  especial  need  to  develop  the 
band  of  light,  as  the  case  can  be  just  as  readily  corrected  by  meas- 
uring the  refraction  in  the  two  principal  meridians  after  the  manner 

of  dealing  with  a  simple  hyperopic  or  my- 
opic case,  but  in  astigmatic  eyes  with  oblique 
axes  the  band  must  be  developed  to  ascer- 
tain the  inclination  of  the  axes. 

In  regular  astigmatism  the  refraction  is 
the  same  in  different  parts  of  the  pupil  in 
any  given  meridian,  though  differing  in  dif- 
ferent meridians.  In  case's  of  spherical  aber- 
ration and  irregular  astigmatism  the  refrac- 
tion differs  in  different  parts  of  the  pupil  in 
the  same  meridian.  All  eyes  present  varia- 
tions of  this  kind  which  form  an  obstacle  to 
the  measurement  of  refraction  by  retinos- 
copy  or  by  any  other  method.  Inasmuch 
as  the  refraction  of  the  eye  with  irregular  as- 
tigmatism differs  in  different  parts  of  the  same  meridian,  there  are 
many  points  of  reversal,  and  the  observer's  eye  being  nearer  some 
than  others  causes  the  pupil  to  appear  broken  up  into  light  and  shade 
without  any  degree  of  regularity,  in  the  place  of  the  homogeneous 
red  reflex  seen  in  other  eyes  by  reflected  light.  On  rotating  the 
mirror  there  is  seen  a  motion  of  the  small  light  and  dark  areas,  some 


RETINOSCOPY.  373 

against  and  others  with  the  mirror.  The  appearance  of  the  eye  with 
irregular  astigmatism  caused  by  corneal  disease  is  shown  in  figure  no. 
I,  and  in  figure  no.  2  the  appearance  presented  by  incipient  cataract. 

In  figure  no.  2  the  darker  areas  are  opacities  in  the  lens,  the  lighter 
ones  shadows  produced  by  irregular  astigmatism,  showing  the  change 
in  the  lens  preceding  senile  cataract.  At  times  the  same  appearance 
is  seen  in  the  eyes  of  young  people,  as  a  congenital  defect,  and  per- 
haps not  increasing  in  years.  If  the  difference  of  refraction  in  differ- 
ent parts  of  the  pupil  is  slight,  the  observer  will  not  notice  the  differ- 
ence in  the  illumination  and  movement  until  he  gets  his  eye  close  to 
the  point  of  reversal.  The  only  way  to  deal  with  irregular  astigma- 
tism by  retinoscopy  is  to  understand  the  optical  principles  involved  in 
the  test,  and  to  apply  them  as  far  as  possible  in  each  case. 

In  cases  of  irregular  astigmatism  one  attempts  to  ascertain  the 
principal  light  area,  that  is  the  one  that  crosses  the  visual  zone  as 
the  mirror  is  rotated,  and  the  refraction  corrected  thereby.  It  is  a 
great  disadvantage  to  have  the  pupil  of  the  irregular  astigmatic  eye 
much  dilated,  as  the  movement  of  light  and  shade  in  the  pupil  is 
rendered  more  confusing.  All  in  all  retinoscopy  in  irregular  astig- 
matism is  anything  but  satisfactory. 

The  variation  in  the  refraction  of  the  crystalline  lens  does  not 
proceed  regularly  from  the  center  to  the  equator,  but  the  central 
area  is  comparatively  uniform  over  a  consid- 
erable extent,  and  towards  the  margin  the 
change  in  refraction  becomes  increasingly 
more  marked.  The  behavior  of  the  light  in 
the  center  of  the  pupil  is  what  concerns  us 
in  retinoscopy,  as  it  is  this  area  that  is  used 
in  the  visual  act,  the  periphery  of  the  cornea      ^^  ^.^^^^  .^  ^^^^^^  ^^^^  ^.^^  ^^ 

and    lens    being    shut    out    by    the    iris    in    its    side   light   area  is   seen   to   sweep 

normal  condition,  and  only  exposed  by  dilat-  ^"-"""^  ^he  center  of  the  pupil, 
ing  the  pupil.     In  keratoconus  and  lenticonus,  on  rotating  the  mir- 
ror, the  light  is  seen  to  sweep  around  or  revolve  about  the  center  of 
the  pupil,  in  somewhat  the  same  manner  as  the  spokes  of  a  wheel 


374  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

about  the  hub,  and  besides  there  is  usually  the  appearance  of  irreg- 
ular astig-matism. 

The  concave  mirror  gives  a  feebler  illumination  than  does  the  plane 
mirror  and  is  therefore  not  as  well  adapted  to  the  test  as  a  rule. 
In  irregular  astigmatism  we  can  often  get  better  results  by  use  of 
the  concave  mirror  at  a  closer  distance  than  one  meter.  If  the  test 
is  performed  at  50  cm.  distance  we  deduct  2  D.  (100  -j-  50  =  2)  from 
the  plus  lens  or  add  2  D.  to  the  minus  lens  that  reverses  the  move- 
ment. With  the  concave  mirror  the  movement  of  light  in  the  eye  in 
all  conditions  is  just  the  reverse  of  what  it  is  with  the  plane  mirror  — 
that  is  against  the  rotation  of  the  mirror  in  emmetropia,  hyperopia 
and  myopia  less  than  one  diopter  at  one  meter's  distance. 

With  the  plane  mirror  and  the  original  source  of  light  back  of  the 
patient  —  with  nolens  before  the  eye  or  the  weakest  one  that  re- 
verses the  movement  of  light  in  any  meridian,  the  band  appearance 
of  light  is  seen  to  be  across  the  meridian  of  emmetropia  in  simple 
hyperopic  astigmatism  ;  myopia  in  simple  myopic  astigmatism  ;  least 
hyperopia  in  compound  hyperopic  astigmatism  ;  least  myopia  in  com- 
pound myopic  astigmatism ;  meridian  of  myopia  in  mixed  astigmatism. 

If  the  lens  before  the  eye  is  strong  enough  to  reverse  the  move- 
ment of  light  in  all  directions  the  band  appearan(5e,  though  not  so 
well  defined,  runs  across  the  meridians  at  right  angles  to  those  above. 

The  final  test  in  astigmatism  is  to  bring  the  two  points  of  reversal 
together  at  the  distance  of  one  meter.  To  do  this  the  cylinder  that 
corrects  the  astigmatism  is  placed  before  the  eye  together  with  the 
convex  sphere  which  will  bring  the  point  of  reversal  to  the  desired 
distance.  With  these  lenses  before  the  eye  the  test  is  again  applied. 
The  observer  now  moves  closer  to  and  further  from  the  point  of  re- 
versal and  inspects  the  movement  of  the  light  in  all  meridians  of  the 
eye.  If  reversal  for  all  meridians  occurs  at  the  same  distance  from 
the  eye  the  cylinder  is  correct  in  strength  and  in  position  of  its  axis. 
If,  however,  the  movement  of  light  seems  to  cease  in  one  meridian 
and  to  continue  in  a  meridian  at  right  angles  thereto,  it  is  evident 
that  the  cylinder  chosen  does  not  correct  the  astigmatism.     If  the 


RETINOSCOPY.  375 

remaining  astigmatism  has  the  same  principal  meridians  as  those 
already  ascertained,  the  direction  of  the  axis  of  the  cylinder  is  correct, 
but  its  strength  is  not  right.  Whether  the  strength  needs  to  be  in- 
creased or  diminished  will  appear  from  the  fact  that  the  more  myopic 
meridian  continues  to  be  more  myopic,  or  that  what  was  before  less 
myopic  has  become  the  more  myopic  meridian.  If  the  principal 
meridians  with  the  cylinder  before  the  eye  do  not  correspond  with 
those  found  primarily,  the  inclination  of  the  axis  of  the  cylinder  is 
incorrect.  If  the  cylinder  is  of  the  right  strength  or  too  weak  its  axis 
needs  to  be  turned  towards  the  axis  of  a  similar  cylinder  which  would 
correct  the  remaining  astigmatism.  If  the  cylinder  before  the  eye  is 
too  strong,  its  axis  needs  to  be  turned  towards  the  axis  of  a  cylinder 
of  opposite  kind  that  would  correct  the  remaining  astigmatism. 

Measurement  of  Accommodation.  —  Retinoscopy  affords  the  only 
objective  method  at  our  disposal  for  the  measurement  of  range  and 
amplitude  of  accommodation.  This  is  important  in  cases  of  suspected 
paralysis  of  the  ciliary  muscle  in  children,  and  all  for  whom  the  sub- 
jective tests  can  not  be  relied  upon,  and  in  eyes  with  imperfect  vision. 

The  patient  directs  his  gaze  at  some  large  letters  hung  upon  the 
wall  opposite  in  a  partially  darkened  room,  in  such  a  position  that 
the  visual  axis  of  the  eye  under  the  examination  shall  pass  as  close 
as  possible  to  the  eye  of  the  observer.  The  refraction  is  then  meas- 
ured and  a  lens  placed  before  the  eye  that  will  bring  the  point  of  re- 
versal for  all  meridians  at  a  distance  of  a  meter  or  a  little  less.  The 
finger  or  the  point  of  a  pencil  is  then  held  at  about  the  near  point 
of  convergence,  and  in  the  visual  line  so  that  the  direction  of  the 
visual  axis  shall  not  be  changed  during  the  test.  The  refraction  is 
again  measured  with  the  eye  adjusted  for  the  near-point  and  the  in- 
crease in  myopia  equals  the  amount  of  accommodation  effort.  The 
observer  can  tell  whether  the  patient  is  exerting  all  his  accommoda- 
tion and  convergent  effort  by  watching  the  other  eye. 

The  results  of  retinoscopy  should  be  confirmed  by  the  use  of  the 
trial  case  whenever  possible.  If  the  lines  on  the  astigmatic  dial  are 
not  all  alike  the  cylinder  of  the  sphero-cylindrical  combination  before 


376 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


the  eye  should  be  made  stronger  or  weaker  as  the  case  may  be  until 
they  are.  The  sphere  of  the  combination  should  then  be  altered 
until  the  best  vision  is  obtained.  If  there  is  any  doubt  about  the  in- 
clination of  the  combined  cylinder  it  should  be  changed  as  the  patient 
looks  at  the  test-type  and  the  position  of  the  best  vision  decided  upon. 
To  Study  the  Test.  — To  properly  study  the  test  the  student  should 
begin  with  known  conditions  of  refraction,  and  study  the  movement 
of  the  light  in  the  eye  from  known  distances.  He  should  study  care- 
fully the  erect  and  the  inverted  movements  from  within  and  beyond 
the  point  of  reversal.  Only  by  making  himself  familiar  with  the 
var)^ing  appearances  of  the  light  and  shade  in  the  pupil  can  he  ever 
hope  to  become  efficient  in  the  application  of  retinoscopy  to  the 
measurement  of  refraction  errors.  The  best  way  to  do  this  is  to 
provide  himself  with  a  retinoscopic  artificial  eye.  The  cut  below 
illustrates  the  Thorington  retinoscopic  eye.  Accompanying  the  in- 
strument are  several  lenses, 
for  the  study  of  aberration 
and  irregular  astigmatism*  in 
its  various  manifestations. 

To  aid  in  understandinor 
the  optical  principles  in- 
volved in  the  test,  one  may 
take  a  strong  convex  lens, 
and  a  piece  of  cardboard  with 
an  arrow  upon  it.  Let  the 
lens  represent  the  dioptric 
system  of  the  eyeball  and  the 
arrow  upon  the  card  the  ret- 
ina and  light  area  upon  it. 
The  card  is  held  a  little  fur- 
ther from  the  lens  than  its 
focal  distance  and  the  arrow 
viewed  through  the  lens  from  varying  distances.  Nearer  the  lens  an 
erect  image  of  the  arrow  will  be  seen,  blurred  of  course  and  further 


RETINOSCOPY. 


zn 


off  an  inverted  image,  and  between  the  two  points  the  point  of  re- 
versal, a  place  where  no  distinct  image  at  all  can  be  gotten.  The 
movement  of  the  light  upon  the  retina  may  be  gotten  by  moving  the 
card  a  little  from  side  to  side.  The  appearances  presented  in  astig- 
matism may  be  illustrated  by  using  a  round  dot  for  the  object,  and 
combining  with  the  spherical  lens  a  cylindrical  lens.  The  enlarge- 
ment of  the  dot  as  the  point  of  reversal  is  approached  and  its  dimi- 
nution as  that  point  is  departed  from  together  with  its  increased  dis- 
tinctness, are  to  be  noted.  The  combination  of  dot  and  lens  will  also 
beautifully  demonstrate  the  phenomenon  of  aberration,  with  the  cen- 
tral and  peripheral  areas  of  different  movement,  the  one  an  erect  and 
the  other  an  inverted  image. 

In  using  the  artificial  eye  any  amount  of  regular  ametropia  may 
be  made  by  shortening  or  lengthening  the  eye  according  to  the  scale 
upon  the  telescopic  tube.  Astigmatism  is  made  by  placing  a  cylin- 
der in  the  clip  in  front  of  the  eye.  It  should  always  be  remembered 
that  hyperopic  astigmatism  is  made  by  the  use  of  a  concave  cylin- 
drical lens  and  vice  versa  unless  the  student  will  be  puzzled  by  the 
appearances  presented. 

For  the  practice  of  retinoscopy,  the  media  of  the  eye  under  exami- 
nation must  be  comparatively  transparent.  A  slight  but  diffused 
clouding  of  cornea  —  incipient  cataracts  and  opacities  of  the  vitreous 
body  —  interfere  greatly  and  often  render  the  test  impossible  even 
when  the  vision  is  not  greatly  reduced.  In  such  cases  the  trial  case, 
rod  optometer  and  ophthalmometer  have  to  be  relied  upon. 

Reference  to  the  figure  on  page  350  shows  that  it  makes  no  differ- 
ence what  the  refraction  of  the  eye  of  the  observer  is,  as  the  rays  i , 

2  and  3,  4  entering  the  eye  at  ,^ 

iVand  N'  respectively,  stimu-      /^  \^     ^,  \    /     ^^^__^-^ 

late  the  same  portion  of  the    p^^^-^^^^^^^IZIIl^-^ 

fundus    of    the    eye    whether    U=^^I^irlZ^^]Ti::r^^ 

there  is  hyperopia,  emmetro-     \  V'     ^'   /  y^    -^ — ,__ 

pia  or  myopia.     An  inherent        ^^ -^ 

refraction  error  of  the  observer  therefore  could  not  reverse  the  move- 


378 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


ment  of  light  in  the  observed  eye.  The  same  is  true  of  artificial 
myopia  produced  in  the  observer  by  placing  a  convex  lens  of  any 
strength  before  the  eye.  No  matter  what  the  strength  of  the  plus 
lens  the  relation  of  the  rays  entering  the  eye  is  not  changed.  But 
this  is  not  the  case  in  artificially  produced  hyperopia,  for  when  a 
minus  lens  of  about  5  D.  is  placed  before  the  eye  of  the  observer, 
the  entering  rays  are  diverged  so  that  rays  2  and  4  stimulate  the 
upper  part  of  the  fundus  of  the  eye  at  A^and  N'  respectively. 

The  concave  lens  diverges  the  rays  i  and  2,  to  i'  and  2',  which 
stimulate  the  upper  and  the  lower  part  of  the  fundus  respectively, 
thus  reversing  the  apparent  movement  of  the  light  in  the  eye  under 
examination.  If  the  convex  lens  before  the  eye  was  strong  enough 
to  bring  rays  i  and  2  to  a  focus  anterior  to  the  cornea,  and  the  eye 
refractive  enough  to  then  transpose  the  rays  as  they  impinged  upon 
the  retina,  the  movement  would  be  inverted  by  the  convex  lens  ;  but 

this  is  impossible,  for  suppose 
that  the  lens  was  at  6  mm. 
from  the  cornea  and  the  focus 
of  the  rays  4  mm.  anterior  to  it, 
the  eye  to  bring  these  rays  to- 
gether upon 'the  fundus  would 
need  to  be  250  D.  refractive 
(1,000/4=250  D.),  and  of  a  greater  amount  than  this  to  cross 
them.  Such  ocular  refraction  does  not  exist,  i  and  2  are  focused  at 
Fhy  L. 

If  the  eye  was  250  D.  refractive,  the  light  diverging  from  point  F 
would  be  focused  at  b  and  at  O  if  still  more  refracted,  transposing 
the  relation  of  the  rays. 


CHAPTER  XXV 

OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY 

All  the  light  that  enters  a  lens  from  an  object  does  not  aid  in  the 
formation  of  its  image,  but  some  undergoes  reflection  at  the  surfaces 
of  the  lens,  either  passing  out  again  and  becoming  lost,  or  after  being 
reflected  by  the  posterior  surface  of  the  lens  to  the  anterior,  passes  out 
of  the  lens  behind  and  interferes  with  the  distinctness  of  the  image. 
The  incident  rays  are  then  divided  into  three  portions  :  the  useful  or 
image-forming  rays,  the  lost  or  those  that  pass  out  anteriorly,  and 
the  harmful  rays  that  interfere  with  the  distinctness  of  image,  pass- 
ing out  of  the  lens  posteriorly  (see  figure). 

The  harmful  rays  may  enter  the  eye  as  it  is  observing  the  image 
formed  by  the  useful  rays,  causing 
annoyance  because  it  does  not  contri- 
bute to  the  formation  of  the  image. 
In  a  simple  lens  about  8  per  cent,  of 
light  is  lost  by  reflection  and  much 
more  in  complicated  apparatuses. 
The  harmful  light  represents  only 
about  one  five-hundredth  of  the  in- 
cident light.  In  ophthalmometry  about  t^t,  per  cent,  of  light  is  lost 
by  reflection.  The  eye  loses  less  light  than  any  other  optical  in- 
strument, only  about  2  per  cent.  The  useful  light  forms  the  ret- 
inal image ;  the  lost  light  forms  four  images  of  reflection  from 
the  dioptric  surfaces  of  the  eye,  and  the  harmful  light  a  series  of 
false  images  of  which  one  only  is  visible.  The  images  formed  by  the 
lost  light  are  called  the  images  of  Purkinje.  They  are,  as  said,  four 
in  number,  one  from  each  surface  of  the  cornea  and  each  surface  of 
the  lens.     They  were  discovered  by  the  scientist  whose  name  they 

379 


380  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

bear,  but  the  second  one,  that  from  the  posterior  surface  of  the  cornea, 
was  lost  sight  of  until  Tscherning  again  called  attention  to  it. 

The  Manner  of  Observing  the  Images  of  Piirkinje. —  The  bright- 
est image  is  formed  by  the  anterior  surface  of  the  cornea,  and  is 
easily  observed.  To  see  the  second  image,  that  formed  by  the  pos- 
terior surface  of  the  cornea,  one  places  himself  a  little  in  front  of  and 
to  one  side  of  the  eye,  which  he  examines  with  a  magnifying  glass 
without  focusing  the  light  upon  the  eye.  Examining  the  corneal 
image  of  the  flame  we  see  as  it  approaches  the  edge  of  the  cornea 
that  it  is  accompanied  by  a  smaller  image  situated  near  it.  The 
smaller  image  is  situated  between  the  larger  one  and  the  pupil  which 
indicates  that  the  posterior  surface  of  the  cornea  is  more  curved  than 
the  anterior.  If  two  lamps  are  used,  one  on  each  side  and  the  dis- 
tance between  them  considered  as  the  object,  we  shall  see  that  the 
distance  separating  the  smaller  images  is  less  than  that  separating 
the  larger  images,  indicating  that  the  curvature  of  the  posterior  sur- 
face of  the  cornea  is  greater  than  that  of  the  anterior.  At  the  center 
of  the  cornea  the  smaller  image  is  not  visible  as  it  is  hidden  behind 
the  larger  one.  The  image  formed  by  the  anterior  surface  of  the 
crystalline  lens  always  preserves  a  more  or  less  diffused  appearance, 
due  to  the  fact  that  the  index  of  refraction  of  the  lens  varies  in  its 
superficial  layers.  To  properly  observe  it,  the  observed  eye  should 
look  so  as  to  bisect  the  angle  between  the  light  and  the  examiner. 
After  having  observed  it  the  light  may  be  concentrated  upon  the  eye, 
the  image  is  thereby  magnified  and  fills  the  entire  pupil.  The  fourth 
image  is  seen  under  the  same  conditions  as  the  preceding  one  and 
offers  little  difficulty.  This  image  being  inverted  moves  in  a  direc- 
tion contrary  to  the  others.  To  make  a  more  accurate  study  of  these 
images  the  ophthalmophakometer  of  Tscherning  may  be  used 
(which  see). 

All  the  reflected  rays  that  emerge  from  the  eye  to  form  the  four 
catoptric  images,  with  the  exception  of  those  of  the  first  image,  meet 
surfaces  which  again  reflect  a  part  of  the  light.  This  light  is  very 
feeble  for  most  of  the  surfaces.    It  is  only  at  the  anterior  surface  of  the 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY.      38 1 

cornea  that  there  is  reflected  enough  light  to  be  visible.  Thus  there 
are  two  more  images  formed  ;  a  fifth,  formed  by  a  first  reflection  from 
the  anterior  surface  of  the  crystalline  lens  and  a  second  from  the 
anterior  surface  of  the  cornea,  and  the  sixth,  due  to  a  first  reflection 
from  the  posterior  surface  of  the  lens  and  a  second  reflection  from 
the  anterior  surface  of  the  cornea.  These  images  are  entirely  sub- 
jective, as  the  rays  forming  them  return  towards  the  retina.  The 
fifth  image  is  furthermore  entirely  theoretical.  It  ought  to  be  situ- 
ated near  the  posterior  surface  of  the  crystalline  lens,  but  no  trace  of 
it  can  be  seen.  The  sixth  image  is  as  a  rule  easy  to  observe.  In  a 
semi-darkened  room  a  distant  object  is  fixed,  while  one  moves  a 
lighted  candle  from  side  to  side,  in  front  of  and  a  little  to  one  side 
of  the  eye.  The  candle  is  made  to  approach  and  recede  from  the 
visual  line  but  never  reaching  it.  There  is  then  seen  projected  on 
the  opposite  side  of  the  visual  line  a  blurred  inverted  image  of  the 
flame.  If  the  refractive  index  of  the  superficial  layers  of  the  crystal- 
line lens  had  been  higher  the  image  would  be  brighter  and  hence 
more  annoying.  The  brightness  of  this  image  is  really  about  1/40,- 
000  of  that  of  the  useful  image.  By  the  study  of  the  images  of 
Purkinje  we  can  locate  the  internal  refracting  surfaces  of  the  eye. 
These  images  have  no  function  so  far  as  the  eye  is  concerned,  but 
are  of  importance  only  in  physiological  optics.  Their  study  consti- 
tutes ophthalmometry,  by  which  term  we  mean  the  mensuration  of 
the  surfaces  of  the  dioptric  media  of  the  eye,  and  unless  otherwise 
indicated  keratometry  or  the  mensuration  of  the  anterior  surface  of 
the  cornea  is  implied. 

The  curvature  of  the  posterior  surface  of  the  cornea  does  not  enter 
as  a  causative  factor  in  astigmatism  to  any  great  extent  as  the  index 
of  the  cornea  and  that  of  the  aqueous  humor  behind  are  practically 
the  same  as  it  is  equally  curved  as  a  rule  in  all  directions.  There  are 
then  practically  but  three  surfaces  that  may  give  rise  to  astigmatism, 
namely,  the  anterior  surface  of  the  cornea  and  the  anterior  and 
posterior  surfaces  of  the  crystalline  lens.  We  measure  and  compare 
the  curvature  of  these  surfaces  in  different  meridians  by  aid  of  their 


382 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


catoptric  images.  Any  inequality  of  the  curvature  of  the  anterior 
surface  of  the  cornea  in  different  meridians  may  be  recognized  by  Pla- 
cido's  disc.  This  instrument  consists  of  a  poHshed  disc  of  aluminium, 
about  eight  inches  in  diameter,  upon  which  are  painted  concentric 


circles  in  black  enamel.  The  instrument  is  held  about  ten  inches 
from  the  eye  and  the  light  reflected  from  it  upon  the  cornea.  Dis- 
tortion of  the  reflected  images  of  the  circles  indicates  astigmatism.  In 
regular  astigmatism  the  circles  appear  as  ovals,  the  long  axes  corre- 
sponding to  the  meridian  of  least  refraction,  that  is  the  greatest  hype- 
ropic  or  the  least  myopic  meridian,  for  the  flatter  the  curve  of  a  mirror, 
the  longer  the  radius  of  curvature,  and  the  larger  the  reflected  image. 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY. 


;83 


If  the  sight-hole  of  the  keratoscope  is  not  at  the  same  height  as 
the  pupil  of  the  observed  eye,  and  if  the  disc  is  not  held  parallel  to 
the  iris  of  the  eye  under  examination,  the  reflected  images  will  ap- 
pear oval  and  astigmatism  thus  simulated.  Claiborne's  hand  oph- 
thalmometer is  a  modification  of  the  Placido  disc,  having  in  addition 
radiating  lines  as  seen  in  the  figure  indicating  the  preferred  posi- 
tions in  hyperopic  and  in  myopic  astigmatism,  and  a  revolving  double 


The  Javal-Schiotz  Ophthalmometer. 

carrier  fastened  to  the  back  of  the  disc,  which  holds  a  strong  mag- 
nifying lens  and  a  short-focus  retinoscopic  mirror.  The  radiating 
lines  enable  the  examiner  to  readily  tell  the  direction  of  the  elonga- 
tion of  the  reflected  circles.  The  lens  back  of  the  disc  magnifies  and 
sharpens  the  image.  Both  of  these  instruments  are  of  litde  value,  as 
a  slight  tilting  of  the  disc  causes  the  appearance  of  astigmatism.     In 


384 


THE   EYE,    ITS    REFRACTION   AND   DISEASES. 


irregular  astigmatism  when  it  was  impossible  to  in- 
telligently use  the  ophthalmometer  of  Javal  and 
Schiotz  on  account  of  the  great  distortion  of  the  re- 
flected images  of  the  mires,  they  are  of  utility  in 
deriving  some  information  as  to  the  meridians  of  the 
greatest  and  the  least  refraction. 

The  ophthalmometer  of  Javal  and  Schiotz  enables 
one  to  diagnose  and  to  measure  with  accuracy  the 
corneal  astigmatism. 

The  improved  ophthalmometer  consists  of  a  tele- 
scope mounted  upon  an  upright  column,  with  a  rack- 
and-pinion  movement  enabling  the  operator  to  easily 
adjust  the  height  of  the  instrument.  The  column 
rests  upon  a  japanned  base,  upon  which  it  moves 
backward  and  forward,  by  rack-and-pinion  movement, 
in  focusing  the  instrument.  At  the  base  of  the  up- 
right there  is  a  rotating  joint  for  the  lateral  adjust- 
ment of  the  instrument.  The  large  steel  disc  seen 
in  the  cut  is  to  protect  the  eyes  of  the  observer  from 
the  light. 

The  telescope  consists  of  an  adjustable  eye-piece 
D,  and  an  achromatic  objective  of  a  compound  char- 
acter. The  objective  carries  between  its  lenses,  A 
and  C,  a  Wollaston  birefringent  prism  B,  made  of 
two  pieces  of  quartz  cut  at  opposite  axes,  in  such  a 
manner  as  to  double  the  image  reflected  by  the  cor- 
nea. At  the  point  Jtr,  the  conjugate  focus  of  the  objec- 
tive lens,  a  crossed  spider  web  is  placed,  upon  which 
the  ocular  is  focused,  and  upon  which  the  image  is 
centered.  The  large  metallic  disc  in  the  older  in- 
struments had  graduations  upon  its  anterior  face 
from  o  to  1 80  degrees,  to  indicate  the  axes  of  any 
existing  astigmatism.  The  figures  were  painted  re- 
versed so  that  they  were  read  correctly  when  reflected  by  the  cornea. 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY.      ^8^ 


O^D 


There  was  also  upon  the  disc  a  series  of  concentric  circles,  so  ar- 
ranged that  when  reflected  by  the  cornea  they  appeared  equidistant 
and  showed  the  size  of  the  corneal  image.  These  graduations  are 
replaced  in  the  newer  models  by  a  small-graduated  dial  attached  to 
the  telescope  behind  the  large  disc.  In  front  of  the  telescope  and  at- 
tached to  it  there  is  an  arc  graduated  upon  its  outer  edge  in  half  cen- 
timeters, to  determine  the  size  of  the  reflected  image,  and  upon  the 
inner  edge  from  5-13,  to  indicate  the  radius  of  curvature  of  the 
cornea  in  the  meridian  in  which  the  arc  stands.  Upon  this  arc  travel 
two  targets  or  mires,  moved  along  the  arc  by  means  of  a  milled 
head  upon  the  rear  of  the  large  disc.  One  mire  consists  of  eight 
white  steps  and  is  called  the  step  mire.  The  other  one  is  of  the 
form  of  a  parallelogram,  six  centimeters  long  and  three  wide. 
Through  each  there  runs  a  black  line,  which  appears  continuous  in 
the  reflected  image.  The  two  pointers  at  the  side  of  the  mires  indi- 
cate the  position  of  the  axis  of  the  correcting  cylinder,  in  the  primary 
position  in  hyperopic  astigmatism  and  in  the  secondary  position, 
the  axis  of  the  correcting  cylinder  for  myopic  astigmatism.  Upon 
the  back  of  the  large  disc  there  is  a  small  scale  to  correspond  with 
the  reading  upon  the  arc,  which  is  indicated  by  a  white  line  upon 
the  foot  of  the  step  mire.  Day  light,  gas,  or  electric  light  may  be 
used  to  illuminate  the  mires.  In  either  case  the  cornea  must  be  in 
the  shade,  as  any  light  falling  upon  it  interferes  with  the  distinct- 
ness of  the  images  of  the  mires. 

Attached  to  the  swinging  eye-shield  upon  the  head  rest  of  the 
instrument  is  an  artificial  glass  cornea  of  about  the  curvature  of  the 
average  cornea.  It  is  very  useful  in  testing  the  accuracy  of  the 
ophthalmometer  and  for  practice  in  the  use  of  the  instrument.  Any 
amount  of  astigmatism  may  be  made  by  placing  the  proper  cylinder 
in  the  graduated  cell  below  the  artificial  cornea,  and  any  inclina- 
tion given  to  the  axis  of  the  cylinder.  As  the  lens  and  the  cor- 
nea do  not  occupy  the  same  focal  plane,  the  reading  of  the  instru- 
ment differs  from  the  focus  of  the  lens  according  to  the  following 
scale  : 
25 


386 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


Focus  of  Trial  Lens. 

Result  with  Artificial  Cornea. 

Focus  of  Trial  Lens. 

Result  with  Artificial  Cornea. 

.25 

.12 

2.50 

1-75 

•SO 

.25 

2.75 

2.00 

•75 

•50 

3.00 

2.00 

I.CX) 

.62 

350 

2.50 

1.25 

•75 

4.00 

3.00 

1.50 

I.OO 

4.50 

325 

I-7S 

I- 25 

5.00 

3-50 

2.00 

1.50 

5-50 

4.00 

2.25 

1-75 

6.00 

4-5° 

Manner  of  Using  the  Ophthalmometer.  —  The  examiner  should 
first  adjust  the  telescope  by  looking  through  it  and  turning  the  eye- 
piece, until  the  crossed  hairs  are  in  perfect  focus,  then  rotate  the 
telescope,  so  that  the  arc  bearing  the  mires  is  horizontal,  told  by  the 
pointers  upon  dial  being  at  o  and  90.  Adjust  the  head  of  the  patient 
by  means  of  the  chin  rest  so  that  the  eyes  are  upon  the  level  with  a 
painted  line  on  the  side  of  the  head-piece,  with  the  forehead  pressed 
against  the  top  of  the  head-piece.  See  that  the  eyes  are  horizontal 
by  sighting  through  the  slit  in  the  disc  above  the  telescope.  Cover 
one  eye  of  the  patient  with  the  swinging  eye-shield  attached  to  the 
head  rest,  and  sight  the  telescope  on  the  eye  to  be  examined  by  look- 
ing along  the  upper  side  of  the  barrel  of  the  instrument.  When  once 
pointed  to  the  cornea  adjust  the  instrument  by  faising  or  lowering, 
and  focus  by  moving  it  backward  and  forward  until  the  images 
of  the  mires  reflected  from  the  cornea  come  clearly  into  view.  The 
corneal  reflection  of  the  mires  is  doubled  by  the  instrument,  and  of 
the  four  mires  seen  in  the  field,  only  two  are  to  be  taken  into 
account,  they  are  the  steps  and  parallelogram  that  appear  in  close 
proximity  in  the  center  of  the  field.  The  images  of  these  are  made 
to  fall  upon  the  point  of  intersection  of  the  crossed  hairs  in  the 
ocular,  by  manipulating  the  telescope.  The  mires  are  moved  along 
the  arc  by  means  of  the  milled  head  on  the  back  of  the  large  dial, . 
until  the  two  middle  images  are  just  in  contact  by  their  edges,  and 
the  telescope  is  then  rotated  until  the  bisecting  line  through  each 
forms  a  continuous  line  if  it  is  not  already  so.  This  is  now  what  is 
termed  the  primary  position.     The  telescope  should  not  be  turned 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY. 


387 


further  to  the  right  or  to  the  left  than  45  degress  in  finding  the 
primary  position,  or  astigmatism  with  the  rule  becomes  confounded 
with  that  against  the  rule  and  vice  versa.  In  regular  astigmatism  the 
lines  always  become  continuous  within  45  degrees  to  the  right  or  to 
the  left  of  o.  The  axis  of  the  primary  position,  which  is  the  axis  of 
one  principal  meridian  is  noted  upon  the  disc  behind  the  upright  of 
the  instrument  according  to  the  position  of  the  hand  that  bears  the 
plus  sign. 

The  appearance  of  the  reflection  in  the  primary  position  is  shown 
in  the  cut. 


After  the  primary  position  is  ascertained  the  telescope  is  rotated 
through  90  degrees  to  the  secondary  position  by  grasping  the  bar- 
rel of  the  instrument  behind  the  upright  and  turning  it  towards 
the  left  hand,  against  the  direction  that  the  hands  of  a  watch 
move.  If  there  is  no  corneal  astigmatism  present  the  mires  will 
remain  in  contact  throughout  the  revolution,  but  if  astigmatism 
is  present  the  images  of  the  middle  two  mires  will  be  seen  to 
separate  or  overlap.  The  parallelogram  mire  appears  to  overlap 
the  step  mire,  as  seen  by  the  increased  whiteness  or  milkiness 
of  the  steps  overlapped.  If  the  astigmatism  is  regular  the  line 
through  each  mire  will  be  continuous,  and  the  mires  of  their  proper 
shape,  while  if  the  lines  through  the  middle  of  each  are  not  con- 
tinuous in  the  secondary  position,  or  if  the  mires  .appear  much  dis- 
torted in  the  reflection,  there  is  irregular  corneal  astigmatism 
present.  If  the  mires  overlap  as  the  telescope  is  turned  to  the 
secondary  position,  there  is  astigmatism  with  the  rule,  while  if  they 


;88 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


separate  there  is  astigmatism  against  the  rule, 
but  there  is  no  way  to  tell  whether  this  astig- 
matism is  hyperopia  or  myopic.  The  figure 
opposite  shows  four  diopters  of  astigmatism 
with  the  rule,  each  step  overlapped  denoting 
one  diopter. 

If  the  mires  separate  on  rotating  to  the  sec- 
ondary position,  they  should  be  brought  into 
contact  again,  and  the  telescope  turned  back  to 
the  primary  position,  when  they  will  be  seen 
to  overlap,  and  the  amount  of  overlapping  will 
indicate  the  amount  of  astigmatism  against  the 
rule. 

The  amount  of  astigmatism  can  also  be  read 
off  on  the  graduated  scale  on  the  back  of  the 
large  dial  with  graduations  corresponding  to 
those  on  the  arc,  as  follows  :  See  that  the  brass 

pointer  with  knob  (secondary  pointer)  on  back  of  dial  covers  the 

lower  pointer  (primary  pointer)  exactly,  so  that  the  pin  on  the  lower 

pointer  fits  into  the  hole  of 

the  secondary  pointer  (see 

figure   C).      (This  is  done 

by  rotating  the  nurled  head 

until     both     pointers    are 

brought    in    line.)      Bring 

the  mires   to   the   primary 

position. 

Turn    the    telescope    90 

degrees   to   the  secondary 

position,    when    in    case  of 

astigmatism  the  images  will 

overlap ;  lift  the  secondary 

pointer  so  that  it  will  stand 

at  right  angles  to  the  dial,  jjg.  c. 


Fig,  D. 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY.      389 

and  move  the  mires  until  they  again  just  touch  as  in  the  primary 
position,  lay  the  secondary 
pointer  against  the  scale,  and 
the  difference  between  the 
two  pointers  will  then  indi- 
cate the  amount  of  astigma- 
tism in  diopters.  To  ascer- 
tain the  amount  of  refraction 
of  the  anterior  surface  of  the 
cornea  in  diopters,  one  must 
add  20  to  the  graduations  of 
diopters  upon  the  arc  or 
upon  the  small  dial  upon  the 
back  of  the  large  disc.  This 
is  necessary  because  in  all 
the  older  instruments  the 
left-hand  mire  was  stationary  and  clamped  at  twenty  degrees  upon 

the  arc,  and  the  mensuration 
has  not  been  changed  in  the 
newer  instruments.  The  rea- 
son that  the  images  of  the 
mires  overlap  in  astigmatism 
with  the  rule  is  as  follows : 

The  mires  are  imaged  by 
the  meridian  of  the  cornea 
in  which  the  arc  carrying  the 
mires  stands.  In  astigma- 
tism with  the  rule  it  will  be 
recalled  that  the  cross  curve 
of  the  cornea  is  flatter — that 
is  its  radius  of  curvature 
is  longer  than  the  vertical 
curve.  The  larger  the  radius  of  curvature  of  a  convex  mirror  which 
the  cornea  represents,  the  larger  the  catoptric  image  and  vice  versa. 


390  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

The  mires  may  be  supposed  to  be  the  extremities  of  an  object.  They 
recede  from  each  other  in  case  the  object  increases  in  size  and  ap- 
proach each  other  in  case  the  object  grows  smaller.  The  doubling 
prism  in  the  instrument  enables  us  to  tell  whether  the  image  has 
increased  or  diminished  in  size.  The  ends  of  the  doubled  image  are 
brought  in  contact ;  the  right-hand  end  of  the  left  image  being  on  the 
right  of  the  left-hand  end  of  the  right  image,  as  will  be  seen  by  refer- 
ence to  the  figure  of  the  mires  upon  the  preceding  page.  If  the  curve 
of  the  cornea  from  above  down  is  sharper  than  it  is  from  side  to  side, 
the  catoptric  image  of  the  mires  will  decrease  in  size  as  the  telescope  is 
rotated,  which  causes  the  step  and  the  parallelogram  in  each  case  to 
approach  each  other.  This  causes  the  mjddle  two  mires,  one  of  each 
half  of  the  double  image,  to  overlap.  The  reading  of  the  instrument 
is  recorded  as  follows :  If  the  astigmatism  is  with  the  rule,  and  the 
secondary  position  at  120  degrees,  and  the  amount  of  astigmatism  i 
D.,  it  is  denoted  thus  :  —  i  D.  C.  ax.  30,  or  -+•  i  D.  C.  ax.  1 20. 

The  proper  sign  belonging  to  each  degree  is  denoted  by  the  signs 
upon  the  pointers  on  the  telescope  moving  around  the  disc,  behind 
the  upright  of  the  instrument.  One  pointer  bears  a  minus  and  the 
other  one  a  plus  sign.  In  some  cases  it  is  impossible  to  bring  into 
a  continuous  line  the  middle  line  of  the  two  mires  on  account  of  ir- 
regular astigmatism  from  scars  of  the  cornea  or  from  conical  cornea. 
Not  infrequently  the  ophthalmometer  indicates  that  the  principal 
meridians  are  not  at  right  angles  to  each  other,  for  example  the 
reading  may  be :  3  D.  C.  ax.  80,  or  3  D.  C.  ax.  180.  In  such  cases 
if  there  is  hyperopia  the  axis  of  the  correcting  cylinder  should  be 
placed  at  80  degrees  and  if  there  is  myopia,  it  should  be  at  1 80  de- 
grees. The  objective  astigmatism  as  measured  with  the  ophthalmom- 
eter is  not  always  equal  to  the  subjective  ascertained  by  means  of 
the  trial  lenses,  on  account  of  the  same  kind  or  of  a  reverse  form  of 
astigmatism  resident  in  the  curvatures  of  the  crystalline  lens  coming 
in  to  influence  the  result.  To  get  as  near  as  possible  to  the  true 
amount  of  astigmatism  subtract  from  .50  to  .75  D.  from  the  corneal 
astigmatism  when  it  is  according  to  the  rule  and  add  the  same 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY.      39 1 

amount  to  the  reading  of  the  ophthalmometer  when  the  astigmatism 
is  against  the  rule.  The  difference  between  the  corneal  and  the  sub- 
jective astigmatism  was  first  noticed  by  Bonders  and  Knapp,  and 
they  attributed  it  to  a  lens  astigmatism.  This  was  hypothetical,  as 
no  one  has  endeavored  to  measure  the  curves  of  the  crystalline  lens 
save  Tscherning.  He  proposes  the  name  supplementary  astigma- 
tism for  that  which  influences  the  corneal  astigmatism.  The  part 
which  it  plays  is  as  follows  according  to  most  observers  : 

1 .  If  there  is  no  ophthalmometric  astigmatism  there  is  usually  to 
be  found  a  small  amount  of  subjective  astigmatism  against  the  rule. 

2.  If  the  reading  is  against  the  rule,  the  subjective  astigmatism  is 
usually  against  the  rule  and  greater  in  amount. 

3.  If  the  ophthalmometric  astigmatism  is  with  the  rule  and  of  a 
value  between  i  and  3  D.  the  subjective  astigmatism  generally  dif- 
fers only  slightly  from  it. 

4.  If  the  ophthalmometer  gives  an  astigmatism  greater  than  3  D., 
the  subjective  astigmatism  is  also  with  the  rule  and  frequently 
greater  in  amount. 

Javal  tried  to  express  the  relation  between  ophthalmometric  astig- 
matism and  subjective  astigmatism  by  the  following  formula  : 

ASi=^ k+p.  As^,  in  which  k  and  /  are  two  constants,  ^  =  .50  D. 
against  the  rule  and  /=  1.25.  Accordingly  we  have  the  following 
relations  : 

Against  the  Rule.  With  the  Rule. 

Astigmatism,  ophthalmometric  2  —  I        —  o  —     I  —  2  —  3        —  4      —  5        —  6  Diopters. 
Astigmatism,  subjective  3  — 1.75  —-5  —-75  —2  —3-25  —4-5  —5-75  —7         " 

This  formula  is  entirely  empiric,  as  the  supplementary  astigma- 
tism depends  upon  so  many  factors,  that  it  is  impossible  to  express 
the  relation  in  a  formula. 

Among  the  factors  may  be  mentioned  : 

I .  Deformity  of  the  internal  surfaces,  as  that  of  the  posterior  sur- 
face of  the  cornea,  which  according  to  measurements  made  by 
Tscherning  was  frequently  found  to  be  more  curved  from  above 
down  than  from  side  to  side.     This  deformity  causes  astigmatism 


392  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

against  the  rule,  inasmuch  as  the  posterior  corneal  surface  acts  like  a 
minus  lens  (4.73  D.).  The  same  defect  in  the  anterior  surface  of  the 
cornea  gives  rise  to  astigmatism  with  the  rule.  In  the  few  cases 
measured,  the  anterior  surface  of  the  crystalline  lens  possessed  astig- 
matism with  the  rule  and  the  posterior  surface  astigmatism  against 
the  rule. 

2.  Obliquity  of  the  crystalline  lens  may  give  rise  to  a  small 
amount — about  .50  D  — as  any  obliquity  is  nearly  compensated  for 
by  the  special  structure  of  the  lens,  as  pointed  out  by  Hermann. 

3.  Sectional  accommodation  or  astigmatic  accommodation  may 
overcorrect  the  corneal  astigmatism,  if  such  a  thing  as  astigmatic 
accommodation  exists,  which  is  very  doubtful. 

4.  The  influence  of  the  distance  of  the  correcting  cylinder  from 
the  eye  must  not  be  overlooked,  on  account  of  which  concave  lenses 
are  weaker  and  convex  ones  stronger  than  the  total  astigmatism. 
That  is  a  concave  cylinder  of  greater  strength  and  a  convex  cylin- 
der of  less  strength  is  needed  to  correct  the  subjective  astigmatism 
than  that  indicated  by  ophthalmometry.  Certain  observers  have 
found  that  astigmatism  with  the  rule  often  exceeds  that  found  with 
the  ophthalmometer.  This  is  due  to  the  fact  that  they  use  concave 
cylinders  perhaps  in  their  tests. 

5.  The  most  important  factor  that  influences  supplementary  astig- 
matism, perhaps,  is  irregularity  of  astigmatism  in  different  zones  of 
the  cornea.  This  exists  in  nearly  all  eyes,  and  is  the  cause  of  some 
of  the  indecision  on  the  part  of  patients  in  selecting  the  proper  cylin- 
der when  tested  subjectively.  Furthermore,  the  axes  of  the  objec- 
tive and  subjective  astigmatism  frequently  fail  to  correspond,  as  the 
axes  of  the  astigmatism  of  the  internal  surfaces  are  oblique  to  each 
other  or  to  the  axes  of  the  anterior  surface  of  the  cornea.  The  effect 
is  then  that  of  crossed  cylindrical  lenses  with  oblique  axes.  While 
measuring  with  the  ophthalmometer  the  patient  should  look  direcdy 
into  the  telescope,  unless  one  wishes  to  measure  the  peripheral  por- 
tions of  the  cornea.  The  refraction  of  each  corneal  meridian  may 
be  read  off  from  the  small  dial  on  the  posterior  surface  of  the  large 


OPHTHALMOMETRY   AND    OPHTHALMOPHAKOMETRY.  393 

disc.  The  small  dial  is  graduated  on  its  edge  in  half  diopters  and 
within  in  millimeters  of  radius  of  curvature,  a  pointer  indicating  upon 
the  inner  circle  the  radius  of  the  anterior  surface  of  the  cornea. 
Both  mires  should  be  movable,  as  in  the  Meyrowitz  model  of  ophthal- 
mometer, as  then  the  reflection  of  each  is  obtained  at  the  same  dis- 
tance from  the  center  of  the  cornea,  and  each  mire  equally  distant 
from  the  cornea,  which  is  not  the  case  if  only  one  mire  is  movable, 
as  in  the  old  models,  as  the  instrument  must  be  twisted  to  get  the 
reflection  of  each  mire  at  the  same  distance  from  the  center  of  the 
cornea,  giving  rise  to  inaccuracies.  Reflection  from  the  periphery 
of  the  cornea  shadows  the  presence  of  astigmatism  that  does  not 
enter  into  the  visual  act  save  in  a  number  of  cases  with  widely  dilated 
pupils.  The  plane  of  the  iris  should  also  be  parallel  to  that  of  the 
mires,  and,  as  this  is  not  always  possible,  the  reading  of  the  instru- 
ment is  subjected  to  error. 

All  in  all  the  ophthalmometer  is  disappointing  and  should  not  be 
relied  upon  to  the  exclusion  of  the  trial  case.  In  about  50  per  cent, 
only  does  it  give  the  proper  amount  of  astigmatism  and  in  about  75 
per  cent,  the  true  axis  of  the  subjective  astigmatism,  in  the  writer's 
experience.  After  the  proper  deductions  are  made  it  will  be  found 
of  a  decided  help  in  the  majority  of  cases,  especially  in  ascertaining 
the  axes  of  the  astigmatism.  Some  have  ventured  the  opinion  that 
one  radius  of  curvature  belongs  to  emmetropia  and  that  by  taking 
the  radius  into  account  or  the  distance  it  was  necessary  to  have  the 
telescope  to  bring  the  images  of  the  mires  into  focus  would  give  a 
clue  as  to  the  amount  of  ametropia.  This  is  a  mistake,  for  ametro- 
pias of  curvature  are  rare,  for  as  Javal  has  said  a  mouse  and  an  ele- 
phant may  each  be  emmetropic,  but  their  corneal  radii  must  be  very 
different.  The  radius  of  curvature  of  cornea  varies  from  7  to  8.5 
mm.  in  emmetropes,  the  average  being  7.8  mm.  The  radius  is 
greater  in  persons  of  tall  stature  and  with  large  cranial  circumference. 
Hyperopia  and  myopia  from  altered  corneal  curvature  does  not  exist 
except  in  microphthalmic  eyes  and  those  with  applanatic  corneae, 
keratoconus  or  keratoglobus.     Even  in  high  anisometropia  save  in 


394  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

cases  of  astigmatism  it  is  very  seldom  that  we  find  any  difference  in 
the  radii  of  the  two  corneas. 

The  basis  of  ophthalmometry  is  the  following  formula : 

in  which  F  is  the  focal  length  of  the  mirror,  /  its  catoptric  image, 
D  the  distance  of  the  object  from  the  mirror,  and  O  the  size 
of  the  object  in  linear  dimensions.  If  we  then  know  the  size 
of  the  object  and  the  distance  of  it  from  the  reflecting  surface, 
and  can  measure  the  size  of  the  reflected  image,  the  strength  of 
the  reflecting  surface  can  be  easily  ascertained.  The  size  of  the 
image  may  be  obtained  by  means  of  a  micrometer  scale  placed  in 
the  ocular  of  the  instrument,  but  as  it  is  nearly  impossible  to  keep 
the  eye  perfectly  quiet,  it  is  very  difficult  to  compare  the  image  with 
this  scale.  Young  and  later  Helmholtz  borrowed  a  method  of 
measuring,  already  in  use  in  astronomical  calculations,  and  ap- 
applied  it  to  ophthalmometry,  that  is  the  method  of  doubling 
(Deboulement).  Suppose  that  we  wish  to  measure  the  distance 
between  two  points,  a  and  b.  By  means  of  an  instrument  we  see 
a  and  b  doubled,  then  instead  of  two  points  we  see  four. 

X 


«',     b 


Y 

aa'  =  bb\  and  let  aa'  =  K,  and  ab  =  X. 

If  we  vary  the  amount  of  doubling  until  a'  and  b  coincide,  that  is 
when  ^  =  1^  we  have  obtained  the  distance  between  a  and  b,  if  we 
know  the  amount  of  doubling.  When  a'  and  b  touch  we  say  that  we 
have  obtained  contact.  The  following  methods  may  be  employed  to 
double  the  images : 

I.  A  Maddox  doubling  prism  may  be  used. 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY.      395 

2.  A  plate  of  glass  with  parallel  sides  placed  before  each  half  of 
the  objective,  oblique  to  the  axis  of  the  telescope,  will  double  the 
image  and  render  the  images  clearer  than  when  a  prism  is  used. 

3.  By  sawing  the  objective  in  half  and  displacing  one  half  laterally. 

4.  By  removing  a  vertical  piece  from  the  middle  of  the  objective, 
and  cementing  the  two  remaining  portions  together. 

5.  The  best  method  however  is  that  of  Wollaston,  employing 
doubly  refracting  crystals  made  of  quartz.  The  two  prisms  are 
placed  together  so  that  they  form  a  piece  with  parallel  sides.  One 
prism  is  cut  with  its  axis  parallel  to  the  axis  of  the  crystal  and  the 
other  one  with  its  axis  at  right  angles  to  the  axis  of  the  crystal. 
Each  ray  Gf  light  that  passes  through  the  prism  is  divided  into  two, 
deviation  of  each  being  symmetrical  to  the  incident  ray. 

By  expressing  the  radius  of  curvature  of  the  cornea  in  millimeters 
we  can  obtain  the  refraction  of  the  cornea  in  diopters  from  the  formula: 

viv'  -  I 
R     ' 

Taking  the  index  of  refraction  of  the  cornea  to  be  1.3375  (Tscher- 
ning) 


F=^ 


■3375 


^„^  p  =  .3375  X  '°^  =  337:5  ^„d  R  =  ^^M 
-R-^  and  JJ  -  — ^—  X  — -        ^   ,  ana  yv:        ^   . 

From  this  formula  the  following  table  is  computed : 


Refraction. 

Radius  of  Curvature. 

Refraction. 

Radius  of  Curvature. 

50  D. 

49 
48 

47 

6.75  mm. 

6.89 

7-03 
7.18 

45  D. 
44 
43 
42 

7.50  mm. 
7.67       ■ 
7.85 
8.04 

46 

7.34 

41 

8.23 

In  the  formula 

F= 

0    ' 

the  formula  expressing  the  relation  between  the  size  of  an  image 
formed  by  a  lens  to  that  of  the  object,  substitute  the  value  of  R  just 
found. 


396  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

F=Rl2 

At  the  moment  of  contact  of  the  two  middle  images  the  amount  of 

doubling  is  equal  to  the  size  of  the  image.      Let  a  represent  the 

linear  length  of  one  degree.     If  this  length  must  equal  one  diopter, 

the  object  which  corresponds  to  the  image  /  must  have  the  size  {D)  a, 

ergo: 

,_.  2  ID  (D)  2DI 

^    ^  337-5  337.5 

As  a  must  be  one  degree  long  we  have  : 

i°/2,6o°  =al27rD 


2TrD       2DI 


/_     337-5  _^ 


360°      337.5  360 


94  mm. 


In  order  that  one  diopter  may  correspond  with  one  degree  of  arc, 
the  doubling  of  the  prism  in  the  instrument  must  equal  2.94  mm.,  so 
it  has  been  made. 

Ophthalmometry  is  especially  useful  in  the  higher  degrees  of  astig- 
matism, and  in  oblique  cases,  and  in  those  who  are  unable  for  some 
reason  to  aid  in  the  subjective  examination  with  the  trial  case.  After 
cataract  extraction,  it  would  be  expected  that  the  ophthalmometer 
would  give  most  valuable  information,  as  the  anterior  surface  of  the 
cornea  is  practically  the  only  one  that  gives  rise  to  astigmatism  in  the 
aphakic  eyeball,  but  the  agreement  between  the  subjective  and  the 
ophthalmometric  astigmatism  after  cataract  extraction  is  frequently 
less  than  in  the  normal  eye,  due  partly  to  the  distance  of  the  correct- 
ing glasses  from  the  eye  and  partly  to  the  irregularity  of  the  cornea 
that  remains  after  the  operation. 

The  advantage  of  the  ophthalmometer  of  Javal  and  Schiotz  over 
all  others  lies  in  the  readiness  with  which  one  can  ascertain  the  prin- 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY.      397 

cipal  meridians  by  means  of  difference  of  level.  When  the  mires  are 
in  the  principal  meridians  their  images  are  on  the  same  level,  and  the 
middle  line  through  each  continuous,  but  outside  the  principal  merid- 
ians the  images  are  in  different  planes  and  the  middle  lines  of  the 
mires  not  continuous  in  the  images.  The  greater  the  astigmatism 
the  more  pronounced  is  this  fact. 

The  difference  between  images  produced  by  a  spherical  and  an 
astigmatic  cornea  may  be  illustrated  by  drawing  a  circle  upon  a  piece 
of  paper  with  two  diameters  at  right  angles  to  each  other,  but  oblique, 
and  viewing  it  through  a  convex  spherical  lens  and  a  sphero-cylindri- 
cal combination.  Through  the  convex  lens  which  is  held  at  some  dis- 
tance from  the  eye  the  image  of  the  circle  is  seen  to  conform  exactly 
with  the  object,  the  diameters  appearing  to  be  at  right  angles  to  each 
other.  Through  the  sphero-cylindrical  combination  the  circle  ap- 
pears drawn  out  into  an  ellipse  in  the  direction  of  the  axis  of  the 
combination. 

The  diameters  of  the  ellipse  do  not  appear  any  longer  to  be  at 
right  angles  but  form  obtuse  angles  with  each  other  above  and  below. 
If  the  sphero-cylindrical  combination  is  turned  so  that  the  axis  of  the 
cylinder  coincides  with  one  of  the  diameters  of  the  circle,  the  diam- 
eters appear  at  right  angles  although  the  circle  appears  drawn  out 
into  an  ellipse.  In  the  first  instance  the  image  (of  the  mires)  is  in  the 
plane  of  the  object  (mires)  and  as  the  doubling  of  the  ophthalmometer 
is  in  the  meridian  of  the  mires,  there  is  no  difference  of  level — the 
diameters  of  the  circle  becoming  obtuse  to  each  other  when  looked 
at  through  the  astigmatic  glass  shows  that  the  reflection  from  an 
astigmatic  cornea  (image  of  the  mires)  is  not  in  the  same  plane  as 
the  object  (mires)  and  as  the  doubling  takes  place  in  this  meridian, 
it  follows  that  on  obtaining  contact  the  images  of  the  mires  are  not 
upon  the  same  level. 

The  Ophthalniophakometer. — The  ophthalmophakometer  of  Tscher- 
ning,  as  shown  in  the  cut,  on  next  page,  consists  of  a  small  telescope 
supported  upon  a  stand,  and  an  arc  of  a  radius  of  86  cm.  movable 
about  the  axis  of  the  telescope,  and  graduated  so  that  the  zero  mark 


398 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


coincides  with  the  axis  of  the  telescope.  Upon  the  arc  move  several 
cursors  which  carry  electric  lamps.  Each  lamp  is  enclosed  within  a 
tube,  closed  in  front  by  a  plano-convex  lens,  which  concentrates  the 


light  upon  the  observed  eye.  The  cursor  A  carries  one  lamp  of  six 
volts  while  cursor  B  carries  two  smaller  lamps  upon  a  rod.  The  rod 
C  with  the  bright  face  serves  as  a  fixation  object. 

Measurememt  of  the  Angle  Alpha  (angle  between  the  corneal 
axis  and  the  visual  axis).  —  If,. as  is  often  the  case,  the  major  corneal 
axis  coincides  with  the  optic  axis,  the  angle  alpha  is  included  be- 
tween the  visual  and  the  optic  axes,  but  if  the  corneal  axis  and  the 
optic  axis  do  not  coincide,  then  the  angle  between  the  visual  axis 
and  the  optic  axis  is  called  angle  beta. 

The  arc  of  the  ophthalmophakometer  is  placed  horizontally  and 
the  cursor  B  at  the  zero  graduation  of  the  arc,  so  that  its  two  lamps 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY. 


399 


are  in  the  same  vertical  plane  as  the  objective  of  the  telescope.  The 
patient  looks  towards  the  latter  place.  It  is  clear  that  if  the  dioptric 
surfaces  were  centered  around  the  visual  axis,  we  would  see  six 
images  of  reflection  in  the  same  vertical  line.  The  images  formed  by 
the  posterior  corneal  surface  are  not  visible  in  this  experiment. 

As  a  matter  of  fact,  the  six  Images  are  never  seen  in  the  same 
vertical  plane.  We  always  see,  as  in  the  figure  below,  on  the  right 
the  images  from  the  anterior  surface  of  the  lens  on  one  side,  those 


from  the  posterior  surface  of  the  lens  on  the  other,  and  those  from  the 
anterior  surface  of  the  cornea  in  the  middle. 

The  bright  ball  on  the  cursor  C  should  then  be  fixed,  and  the  cur- 
sor moved  until  the  images  seen  in  the  eye  are  made  to  occupy  the 
same  vertical  plane,  as  nearly  as  possible,  for  it  is  not  possible  to 
get  them  exactly  in  the  same  plane  ;  two  pairs  of  them  will  come  in, 
but  the  third  remains  outside.  This  takes  place  because  the  axis  of 
the  crystalline  lens  does  not  pass  through  the  center  of  the  cornea, 
usually  a  little  above  the  center  of  the  cornea  in  decided  defects  of 
this  kind.     The  optic  axis  now  lies   in  the  vertical  plane  passing 

through  the  objective  of  the  tele- 
scope and  the  angular  displacement 
of  the  fixation  mark  along  the  arc 
indicates  how  much  the  visual  line 
deviates  from  the  optic  axis,  usually 
from  4°  to  7°. 

The  arc  is  now  placed  vertically, 
so  that  the  two  lamps  are  in  a  horizontal  plane.  The  observed  eye 
then  fixes  the  cursor  C  and  the  operator  moves  it  until  the  images 


From 

Ant.  Lens  Surface 

Post.     .. 

Ant.  Corneal    " 


400  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

of  reflection  are  seen  in  line.  The  angle  at  which  the  cursor  C  stands 
marks  the  vertical  deviation  of  the  visual  line,  2°  to  3°  downwards. 
The  figure  shows  the  usual  position  of  the  six  images  of  reflection, 
when  the  eye  fixes  the  objective  of  the  telescope,  the  lamps  being  in 
the  horizontal  plane.  To  measure  the  radii  of  the  internal  refracting 
surface  of  the  eye  ball  we  must  first  determine  the  distance  of  the 
refracting  surface  from  the  summit  of  the  cornea,  or  the  position  of 
the  surface,  and  the  position  of  the  center  of  the  refracting  surface. 
We  can  measure  the  radii  of  the  surfaces  directly,  as  will  be  ex- 
plained, but  it  must  be  remembered  that  all  sizes  that  we  measure 
are  apparent  sizes  only,  and  that  to  find  the  real  sizes  certain  deduc- 
tions are  necessary  according  to  rules  later  laid  down.  To  make 
this  deduction  it  is  necessary  to  know  the  position  of  the  surfaces, 
which  is  necessary  also  that  we  may  be  able  to  combine  the  surfaces 
with  one  another,  so  that  we  may  calculate  the  entire  system. 

DETERMINATION  OF  CENTERS  OF  INTERNAL  SURFACES 

Take  the  anterior  surface  of  the  crystalline  lens  as  an  example, 
and  suppose  that  we  make  the  measurements  in  the  horizontal  direc- 
tion. The  pupil  should  be  well  dilated.  Place  the  arc  of  the  instru- 
ment horizontally,  and  the  carrier  A  as  far  as  possible  from  the  tele- 
scope. The  lamp  must  be  sufficiently  brilliant  that  its  reflection  from 
the  surface  to  be  measured  may  be  quite  visible.  The  fixation  mark 
is  then  carried  to  a  place  at  which  the  optic  axis  will  bisect  the  angle 
between  the  telescope  and  the  carrier  A.  It  is  necessary,  therefore, 
to  have  previously  calculated  the  value  of  angle  ^.  We  then  move 
cursor  B,  the  lamps  of  which  should  be  feeble,  so  that  their  corneal 
reflections  are  alone  visible,  until  the  crystalline  image  of  A  is  in  line 
with  the  corneal  images  of  B.  We  now  possess  the  elements  neces- 
sary to  calculate  the  distance  of  the  anterior  surface  of  the  crystalline 
lens  from  the  summit  of  the  cornea. 

S^  represents  the  anterior  corneal  surface  and  C  its  center ;  .S'^ 
anterior  crystalline  lens  surface,  and  O,  its  center ;  C  C^  the  optic 
axis  of  the  eyeball,  and  R  the  radius  of  curvature  of  the  cornea. 


OPHTHALMOMETRY   AND    OPHTHALMOPHAKOMETRY.  40 1 

In  the  figure  below,  let  c  represent  half  the  angular  distance 
between  the  telescope  and  the  cursor  A,  and  the  angle  d  half  the 
angular  distance  of  B  from  the  telescope.     Suppose  that  we  know 


the  radius  of  the  cornea  which  is  measured  previously.     In  triangle 
COP: 

sine 
and  for  the  distance  sought 

\        sm  c  J  sin  c 

and 

\  sm  o      sm  a  J 

Unless  great  exactness  is  desired,  the  sines  may  be  replaced  by  the 
arcs. 

Example.  —  Let  the  radius  of  the  cornea  be  7.98  mm.;  the  distance 
oi  A  from  the  telescope  nasally,  28  degrees,  and  the  distance  oi  B 
16.8  degrees  nasally.     We  will  have 

O- O^  =  7.98  (i  -  "'^^^  =  3-16  mm. 
'  ^    V         sm  14°  / 

26 


402 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


The  apparent  depth  of  the  anterior  chamber  would  therefore  be  3.16 
mm.,  from  which  we  can  find  the  true  value  or  depth,  2,-7 Z  "im.,  by 
placing  in  the  formula:  FJ/^  +  F^^jfi  =1,  the  values  F^  =  23.64  ; 
/;=  31.61,  and/ =  —  3.16. 

DETERMINATION    OF    RADII    OF    INTERNAL   SURFACES 

We  place  A  above  the  telescope,  and  move  C  with  the  fixation 
mark  as  far  as  possible  from  the  telescope,  but  so  that  the  image 
does  not  disappear  behind  the  iris  ;  B  is  then  moved  until  the  corneal 


image  of  its  two  lamps  are  on  the  same  vertical  line  as  the  lens 
image  of  A.  The  axis  of  the  telescope  is  now  perpendicular  to  the 
surface  of  the  crystaUine  lens.     In  the  figure,  in  triangle  C'C^O, 

C^C^ :  OC^ ::  sin  d  :  sin  a, 
sin  a 


\        sin  a  J  \ 


sin  a  +  sin  b 


sin  a 


Example. —  Let  ^  =  5.1°  ;    the  distance  of  B  from  the  telescope 
12.4°  temporally  and  Cg.g^  nasally. 


OPHTHALMOMETRY  AND  OPHTHALMOPHAKOMETRY. 

sin  6,2° 


403 


Then  7 


•98  ( 


1  + 


sin  4.8' 


)=,. 


28  mm. 


The  apparent  radius  would  be  18.28  —  3.16  mm.  (apparent  depth 
of  anterior  chamber)  =  15.12  mm. 

Considering  that  we  have  obtained  the  apparent  values  with  refer- 
ence to  the  refraction  of  the  cornea,  we  must  in  the  formula  F^  j  f^  + 
Fi\  fi^  1'  put  F^  =  23.64;  7^2  =  31.61,  andy^  =  —  18.28,  giving  y^  = 
13.78,  the  position  of  the  real  center  and  the  radius  of  the  real 
surface  13.78  —  3.73  (depth  of  anterior  chamber)  =  10.05  ^nm. 

The  posterior  lens  surface  is  located  and  measured  in  the  same 
manner  as  the  anterior  surface,  but  owing  to  the  fact  that  it  lies  very- 
near  the  nodal  point  of  the  eyeball  the  apparent  position  differs  little 
from  the  real  position.  In  regard  to  the  anterior  lens  surface  the  true 
position  or  surface  is  about  5  mm.  behind  the  apparent  surface,  and 
the  radius  of  curvature  of  the  apparent  surface  is  about  15  mm. 
instead  of  10  mm. 

Measureme7it  of  the  Posterior  Corneal  Surface. — The  image  of  the 
more  powerful  lamp  A  is  viewed  as  formed  by  the  posterior  surface 


Catoptric  Image  of  B  from  Cornea 


A.  from  Ant.         _^ 

/f«r^\^r 

^^;■ 

■•      "   A 

Cornea!  Surface    ^^ 

f       ••>^*.          H, 

^^^ 

Post  Surface  of         " 

of  the  cornea  ;  the  images  of  the  two  smaller  lamps  B,  reflected  from 
the  anterior  surface  of  the  cornea  are  brought  into  line  with  the  image 
of  A,  by  sliding  their  carrier  along  the  arc.  The  eye  to  be  measured 
is  directed  at  the  center  of  the  objective  of  the  telescope,  and  the 
cursor  A  is  moved  along  the  arc  until  the  fainter  image  a^  is  seen 
clearly  defined  at  a  little  distance  from  the  brighter  image  a'. 


404  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

The  two  lamps  B  are  now  lighted  and  the  carrier  moved  along  the 
arc  on  the  same  side,  until  the  two  images  reflected  from  the  ante- 
rior corneal  surface  are  seen  in  line  with  the  image  c^.  The  lamps 
are  then  moved  to  the  symmetrical  position  A',  B',  and  the  same  pro- 


cedure repeated.  Referring  to  the  figure  it  will  be  seen  that  a'^'^,  rep- 
resents both  the  length  of  image  of  AA',  reflected  from  the  posterior 
surface  of  the  cornea,  and  of  BB',  reflected  from  the  anterior  surface 
of  the  cornea.  The  difference  between  O',  the  center  of  curvature  of 
the  anterior  surface  of  the  cornea,  and  O^,  the  center  of  curvature  of 
the  posterior  surface  from  the  middle  of  the  arc  is  so  small  that  we 
may  without  sensible  error  assume  the  common  value  of  i  for  both, 
which  by  the  construction  of  the  instrument  is  86  cm. 

The  formula  for  ascertaining  the  radius  of  curvature  of  a  convex 
mirror  is : 

Half  the  radius  of  curvature  _  Distance  of  the  object         „  .    _  ID 
Length  of  the  image  Length  of  the  object  '  ^' 

Designating  the  half  of  the  radius  of  curvature  of  the  anterior  surface 
by  X  and  that  of  the  posterior  surface  by  x',  we  have  for  the  two  sur- 
faces — 

X  I  .   x'  I 

and 


a'^d"     BB"         a'^a"     A  A'' 


OPHTHALMOMETRY   AND   OPHTHALMOPHAKOMETRY.  405 

Dividing  equation  i  by  2,  member  by  member,  we  have: 

BB' 


xjx'  =  AA'jBB'  and  x'  = 


AA' 


The  value  of  x  is  found  with  the  ophthalmometer  and  AA'  and  BB\ 
by  the  scale  upon  the  arc  C. 

The  average  measurements  give  the  following  result,  x'  =0.77  x, 
which  corresponds  to  about  6  mm.,  radius  of  curvature  for  the  pos- 
terior corneal  surface,  or  about  2  mm.  less  than  for  the  anterior  sur- 
face. By  reason  of  the  index  of  refraction  of  the  aqueous  differing 
little  from  that  of  the  cornea,  the  refraction  of  the  posterior  corneal 
surface  is  very  little,  equaling  in  effect  a  negative  lens  of —  4.73  D. 
S.  The  relation  between  the  radii  of  the  anterior  and  the  posterior 
surface  of  the  cornea  is  the  same  everywhere,  the  posterior  surface 
undergoing  a  flattening  at  the  periphery  analogous  to  the  anterior 
surface. 

The  relation  of  the  lights  in  the  pupil  when  measuring  the  poste- 
rior surface  of  the  cornea  is  shown  in  cut  on  page  403, 

The  Direct  Determination  of  Radii. — The  distance  separating  the 
reflected  images  of  the  lamps  may  be  supposed  to  be  the  length  of 
the  image  and  the  distance  between  the  lamps  the  length  of  the 
object.  The  ratio  between  the  distances  separating  the  two  images 
of  a  lamp  placed  at  corresponding  points  on  opposite  sides  of  the  tel- 
escope, is  equal  to  the  ratio  between  the  apparent  radii  of  the  reflect- 
ing surfaces,  according  to  the  formula  7?/ 2  =  ID  I O,  as  O  and  D  are 
the  same  for  all  the  surfaces.  The  measurements  are  accurate  if  we 
make  use  of  two  cursors  similar  to  A  and  two  similar  to  B.  A  is 
placed  so  that  the  reflection  from  the  anterior  surface  of  the  crystal- 
line lens  is  clearly  visible.  B,  whose  lamps  are  feeble,  is  now  placed 
so  that  the  corneal  reflection  is  in  plane  with  one  of  the  images  formed 
by  the  lens.  The  distance  between  the  cursors  A  is  considered  the 
object  for  the  anterior  surface  of  the  crystalline  lens  and  that  sepa- 
rating B,  as  the  object  for  the  anterior  surface  of  the  cornea.     The 


406  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

radii  are  inversely  proportional  to  the  objects  as  the  images  are  alike. 
Knowing  the  radius  of  curvature  of  the  anterior  corneal  surface  by 
previous  measurement,  we  calculate  the  apparent  radius  of  the  ante- 
rior surface  of  the  crystalline  lens.  To  determine  astigmatism  the 
measurements  must  be  repeated  in  the  vertical  meridian.  An  exact- 
ness of  more  than  a  half  of  a  millimeter  can  not  be  guaranteed  in  any 
of  these  measurements.  An  error  of  5^  mm.  in  measuring  the  ante- 
rior corneal  surface  corresponds  to  about  3  D.  whilst  the  same  error 
in  measuring  the  anterior  lens  surface  corresponds  to  ^  D.,  but  as  to 
the  thickness  of  the  lens,  which  is  only  4  mm.,  such  an  error  is  of 
great  importance.  The  practical  result  obtained  by  measurement  of 
the  internal  dioptric  surfaces  does  not  pay  for  the  trouble,  for  each 
surface  must  be  measured  in  at  least  two  meridians,  and  as  each 
surface  calls  for  two  measurements  (of  the  radius  and  of  its  center), 
twelve  measurements  are  necessary,  and  then  one  would  have  to  de- 
duce the  real  values  to  ascertain  the  astigmatism  of  each  surface  and 
finally  to  combine  these  astigmatisms  with  that  of  the  anterior  surface 
of  the  cornea.  This  would  become  more  complicated  if  the  principal 
meridians  of  the  astigmatic  surfaces  did  not  coincide.  It  is  also  like- 
wise impossible  to  measure  the  radius  of  curvature  of  the  posterior 
surface  of  the  cornea  in  the  center,  as  the  reflected  image  from  the 
posterior  surface  of  the  cornea  is  not  visible  at  the  center  of  the 
cornea. 


CHAPTER   XXVI 

TESTS    FOR    HETEROPHORIA 

All  the  tests  for  the  detection  of  inefficiency  of  the  extra-ocular 
muscles  depend  upon  the  fact  that  when  single  binocular  vision  is 
interfered  with,  the  guiding  sensation  ceases  to  operate,  and  both 
eyes  rotate  in  the  direction  in  which  the  strongest  acting  muscle  or 
muscles  pull  them.  All  the  tests  depend  upon  destroying  single 
binocular  vision.  The  simplest  test  is  that  known  as  Von  Graefe's 
screen  test.  The  patient  looks  at  a  candle  flame  at  20  feet  distance, 
or  better  a  round  dot  upon  a  square  piece  of  cardboard,  with  both 
eyes  open.  The  examiner  then  places  a  card  in  front  of  one  or  the 
other  eye,  excluding  it  from  the  visual  act.  If  there  is  balance  of  the 
extra-ocular  muscles  the  eye  behind  the  card  will  remain  perfectly 
directed  towards  the  object  of  observation,  but  if  binocular  vision  is 
ordinarily  maintained  only  by  exerting  an  effort,  the  eye  back  of 
the  card  will  be  pulled  in  the  direction  of  the  strongest  muscle.  This 
fact  will  be  noted  by  a  movement  on  the  part  of  the  eyeball  to  get 
back  into  the  proper  direction  when  uncovered.  This  latter  movement 
is  called  a  redress  movement.  The  redress  is  always  towards  the 
weakest  muscle.  Instead  of  covering  and  uncovering  one  eye,  first 
one  and  then  the  other  may  be  covered  in  quick  succession,  but  not 
too  quickly  for  the  eye,  as  it  is  uncovered  to  adjust  itself  before  the 
screen  is  again  passed  over  it.  In  case  there  is  imbalance  of  the  ex- 
trinsic muscles,  each  eye  will  make  a  redress  movement  when  it  is 
uncovered.  At  the  same  time  the  patient  will  notice  a  shifting  of 
the  object  looked  at,  as  the  screen  is  passed  from  in  front  of  one  eye 
to  the  other.  This  movement  as  observed  by  the  patient  has  been 
called  by  Dr.  Duane  the  parallax  test.  The  examiner  observes  the 
eye  as  it  changes  from  exclusion  to  fixation,  and  neutralizes  the 
movement  with  prisms,  placed  with  their  bases  in  the  direction  of  the 

407 


408  THE   EYE.    ITS   REFRACTION   AND    DISEASES. 

redress,  until  no  more  movement  can  be  seen  by  the  examiner  when 
the  eye  fixes.  The  observation  of  the  patient  is  then  brought  to  bear, 
and  stronger  prisms  used  until  the  patient  can  no  longer  detect  any 
movement  in  the  object,  when  either  eye  is  uncovered. 

The  extent  of  movement  ascertained  by  the  foregoing  tests  is 
called  the  deviation  in  exclusion.  The  same  tests  are  used  to  detect 
any  deficiency  of  convergence.  After  the  refraction  error  is  cor- 
rected a  card  with  a  dot  upon  it  is  held  three  inches  from  the  eyes,  and 
on  uncovering  a  movement  of  the  eyeball  will  take  place  toward  the 
nose  if  convergence  is  below  par,  and  the  patient  will  notice  that  the 
dot  appears  to  move  as  first  one  eye  and  then  the  other  is  screened. 

By  repeating  the  screen  test  with  each  eye  alternately  it  can  be 
told  whether  there  is  habitual  binocular  fixation,  an  alternating  fixa- 
tion or  a  squint  present.  If,  when  the  screen  is  removed,  the  eye 
uncovered  alone  moves,  there  is  heterophoria,  and  not  squint,  pres- 
ent. If  both  eyes  move,  or,  in  spite  of  there  being  an  evident  devia- 
tion, both  eyes  remain  fixed,  there  is  a  squint.  If  in  the  latter  case, 
when  the  left  eye  is  uncovered,  the  eyes  behave  in  the  same  way  as 
they  do  when  the  right  eye  is  uncovered  (both  alike  moving  or  stand- 
ing still)  the  squint  is  alternating.  Lastly,  if  when  one  eye  is  uncov- 
ered both  eyes  move,  and  when  the  other  eye  is  screened  and  uncov- 
ered, both  eyes  remain  steady,  the  squint  is  permanent  and  belongs 
to  that  eye.  The  other  tests  for  heterophoria  depend  upon  the  pro- 
duction of  diplopia. 

A  strong  convex  or  concave  cylinder  is  placed  before  one  eye,  and 
the  patient  looks  at  a  distant  candle  flame.  The  cylinder  causes  the 
flame  to  appear  drawn  out  into  a  long  streak  of  light,  which  is  so 
different  from  the  natural  appearance  of  the  flame  as  seen  by  the 
other  eye  that  the  brain  can  not  fuse  the  two  retinal  images,  espe- 
cially if  a  red  glass  is  placed  before  one  eye,  and  immediately  the 
guiding  sensation  that  keeps  the  two  eyes  properly  directed  ceases 
to  act,  and  the  eye  whose  vision  is  interfered  with  rotates  in  the 
direction  that  the  strongest  acting  muscle  pulls  it.  The  axis  of  the 
cylinder  is  placed  crosswise  before  the  eye  when  one  wishes  to  test 


TESTS    FOR    HETEROPHORIA.  409 

the  laterally-acting-  muscles.  The  streak  of  light  then  appears  to 
run  vertically,  in  the  neighborhood  of  the  candle  flame  seen  by  the 
other  eye.  The  streak  and  the  flame  are  kept  better  before  the 
mind  if  before  one  eye  ;  say  the  one  with  the  cylinder  before  it,  is 
placed  a  red  glass  to  color  the  image  seen  by  that  eye.  If  both  eyes 
are  directed  at  the  flame  of  the  candle,  its  image  will  fall  in  each 
upon  corresponding  parts  of  the  two  retinas,  that  is,  in  the  same  ver- 
tical meridian  in  each.  The  streak  of  light  will  then  appear  to  run 
directly  through  or  over  the  flame  of  the  candle,  each  eye  projecting 
its  image  to  the  same  point  in  space.  If  the  externi  or  the  interni 
are  acting  too  strongly,  the  images  in  the  two  eyes  fall  upon  non-cor- 
responding points  of  the  retinas,  and  the  eyes  project  their  images 
to  different  points  in  space,  the  red  streak  of  light  appearing  to  the 
right  or  to  the  left  of  the  flame.  The  eye  that  sees  the  flame  (the 
one  whose  vision  is  not  interfered  with),  maintains  its  fixation,  keep- 
ing the  image  of  the  flame  upon  its  macula,  while  the  fellow  eye 
deviates.  If  the  cylindrical  lens  is  placed  before  the  other  eye  it  will 
be  seen  that  the  streak  of  light  is  at  the  same  distance  on  the  other 
side  of  the  flame.  This  is  not  always  the  case,  for  in  not  a  few  more 
inefficiency  will  be  demonstrable  in  the  muscles  of  one  eye  than  in 
those  of  its  fellow. 

The  image  of  each  eye  is  always  deviated  towards  the  weaker-act- 
ing muscle.  Suppose  that  the  cylinder  is  before  the  right  eye,  and 
that  the  streak  is  seen  to  the  right  of  the  flame.  The  streak  is  to 
the  right  of  the  flame,  the  muscle  to  the  right  side  of  the  right  eye  is 
the  external  rectus,  which  is  the  weak  muscle.  The  flame  seen  by 
the  other  eye  is  to  the  left  of  the  streak  of  light.  The  muscle  to  the 
left  of  the  left  eye  is  the  external  rectus,  which  is  the  weak  one.  The 
supposed  condition  is  then  one  of  weak  external  recti  or  esophoria, 
a  tendency  on  the  part  of  the  eyes  to  turn  in. 

In  the  figure  the  left  eye  is  represented  as  having  the  cylinder 
before  it,  and  as  there  is  a  lack  of  balance  between  opposing  muscles 
the  eye  turns  in.  as  binocular  single  vision  is  impossible.  The  line 
of  fixation  of  left  eye  is  in  the  direction  x.     The  light  passing  into 


4IO 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


each  eye  does  not  impinge  upon  the  same  portion  of  each  retina.  It 
stimulates  the  macula  in  the  right  eye  and  internal  to  the  macula  in 
the  left  eye,  causing  the  left  eye  to  project  its  image  to  the  left,  the 
right  eye's  image  being  to  the  right.     The  left  eye  projects  its  image 


SEEN  BY 
R.E.  L,E. 


ESOPHORIA 


WITH  CYL.  BEFORE  R  EYE 
L.  EYE 


ESOPHORIA 


R.E. 


WITH  CYL.  BEFORE  R.  EYE 
L.  EYE 


ESOPHORIA 


ESOPHORIA 


in  the  direction  that  x'  would  occupy  if  x  was  brought  to  occupy  the 
position  of  .r'.  This  relation  of  the  streak  of  light  and  flame  is  seen 
in  cases  of  esophoria.  The  relations  of  light  and  streak  in  the  dif- 
ferent named  heterophorias  is  shown  in  cut  above. 


TESTS    FOR    HETEROPHORIA. 


411 


To  test  the  vertically-acting  muscles  the  cylindical  glass  is  placed 
with  its  axis  vertical,  causing  the  streak  of  light  to  run  crosswise, 
which  appears  to  run  through  the  center  of  the  flame  if  there  is 
balance  of  the  vertical  recti.  If  there  is  imbalance  each  eye's  image 
is  deviated  towards  the  weaker  muscle  of  the  corresponding  eye. 

With  cylinder  before  the  left  eye : 


L.  E. 


R.  E. 


R.  E. 


L.  E. 


R.  Hyper 


L.  Hyper 


Maddox  Groove. 


Aiken's  Phoroscope. 


Maddox  Rod. 


If  the  cylinder  was  before  the  other  eye  the  above  forms  of  diplopia 
would  indicate  just  the  opposite  condition  of  the  muscles.  Instead  of  a 
cylinder  being  used  to  distort  the  image  seen  by  one  eye,  Maddox's 
rod  or  groove  is  used  as  a  rule.  Maddox's  rod  consists  of  a  piece  of 
a  glass  rod  set  back  of  a  stenopaic  slit,  in  an  opaque  disc.  The  im- 
proved Maddox  rod  (Aiken's  phoroscope)  consists  of  a  number  of 
small  rods  of  glass  set  side  by  side,  and  backed  by  a  piece  of  red  glass 
to  color  the  image  seen  through  them.  The  rods  of  glass  act  like 
strong  cylinders  to  draw  the  candle  flame  out  into  a  long  streak  of  light. 

Maddox's  groove  upon  red  glass  acts  as  a  strong  concave  cylinder 
in  distorting  the  image  of  the  light,  but  the  multiple  rods  are  preferable 
as  the  streak  seen  through  them  is  much  longer  and  better  defined. 
Maddox  has  devised  another  test,  known  as  the  Maddox  prism  test 
Maddox's  prism  is  a  doubling  prism  made  of  two  six-degree  prisms 


412 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


base  to  base.  The  prism  causes  all  objects  seen  through  it  to 
appear  doubled,  two  candle  flames  are  then  seen  by  the  eye  before 
which  the  prism  is  placed,  if  the  base  line  of  the  prism  intersects  the 

visual  zone — and  the  other  eye 
sees  its  object  between  the  two, 
both  eyes  together  seeing  three 
images  of  the  flame.  When  the 
flames  are  arranged  vertically,  that 
is  when  the  prism  is  placed  with 
its  apices  above  and  below  before 
the  eye,  one  flame  should  be 
directly  under  the  other,  if  there 
is  balance  between  the  laterally- 
acting  recti  muscles,  otherwise 
each  eye's  image  is  deviated  in 
the  direction  of  its  weak  muscle. 
The  prism  is  now  turned  so  that 
the  three  lights  are  side  by  side, 
and  if  there  is  balance  in  action 
between  the  vertically-acting  recti 
the  three  flames  will  lie  in  the  same  horizontal  plane. 

The  test  as  depicted  in  the  figure  above  shows  balance  of  the 
vertically-acting  muscles.  This  test  is  a  good  one  inasmuch  as  in- 
efficiencies of  several  mucles  may  be  detected  at  the  same  time, 
according  to  the  position  of  the  middle  flame,  in  relation  to  the  other 
two.  See  figures  on  next  page,  remembering  always  that  the  image 
is  deviated  towards  the  weaker  muscle  of  the  corresponding  eye. 

A  test  for  insufficiency  of  the  extra-ocular  muscles  can  be  made  by 
producing  diplopia,  by  placing  before  one  or  both  eyes  a  prism 
stronger  than  the  eyes  can  overcome  (a  six-degree  prism  is  a  con- 
venient strength).  Such  a  prism  is  placed  before  the  right  eye — say 
with  its  base  down.  The  image  seen  by  the  right  eye  is  then  above, 
displaced  in  the  direction  of  the  apex  of  the  prism  and  that  seen  by 
the  left  eye  below.     The  two  images  of  the  flame  should  be  directly 


TESTS    FOR    HETEROPHORIA. 

over  one  another  if  there  is  a  balance  between  the  laterally- 
muscles.       In   testing  the 


413 


acting 


RE. 


^ 


R. Hyper. Exophoria 


vertically-acting  muscles,  a 
prism  strong  enough  to 
produce  diplopia  is  placed 
before  one  eye  with  its 
apex  out.  To  measure  / '  1  l  e. 
the  amount  of  weakness 
of  a  muscle,  one  places 
successive  strengths  of 
prisms,  beginning  with  the 
weaker,  before  one  or  the 
other  eye  with  the  base  of 
the  prism  over  the  weaker 

muscle,  until  one  is  ascer-      Exophona  Esophoria 

tained  that  establishes  bal- 
ance of  the  extra-ocular-muscles.  Half  of  the  strength  of  this  prism 
then  represents  the  amount  of  error  in  each  eye.  There  is  no  more 
convenient  apparatus  for  measuring  the  amount  of  error,  as  well  as 
the  extent  of  adduction  and  abduction  than  Risley's  rotating  prism. 
It  consists  of  two  fifteen-degree  prisms,  which  are  revolved  in  op- 
posite directions  by  a  milled  head  screw,  thus 
furnishing  a  prism  the  strength  of  which  can 
be  increased  from  zero  to  thirty  degrees.  It 
is  made  the  diameter  of  a  trial  glass  and  can 
be  placed  before  the  eye  in  the  trial  frame. 
All  of  these  tests  are  faulty  inasmuch  as  the 
objects  seen  are  thrown  out  of  their  relation 
to  each  other  if  the  head  of  the  observer  is  in- 
clined to  the  side,  as  the  axis  of  the  cylinder 
or  rod  must  be  absolutely  horizontal  and  ver 
tical  to  obtain  accurate  results  (must  coincide  with  the  vertical 
meridians  of  the  retinae).  To  obviate  this  possible  error  certain  in- 
struments called  phorometers  have  been  devised.    The  same  methods 


Risley's  Prism. 


414 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


of  testing  are  applied  but  the  test  apparatus  is  held  before  the  eyes 
independent  of  the  head  of  the  patient.  Within  certain  limits  the 
eyes  rotate  by  action  of  the  obliques  so  that  the  vertical  meridians  of 
the  retinas  remain  vertical,  when  the  head  is  inclined  to  the  side,  and 
the  rod  or  what  not  being  always  vertical  before  the  eye  no  discrep- 
ancies can  enter  into  the  calculations.  The  most  widely  used  pho- 
rometer  is  that  devised  by  Dr.  Stevens,  shown  in  the  cut  below  ;  E 
is  a  small  spirit  level  upon  a  horizontal  arm  carrying  a  prism  holder ; 


F  is  leveling  screw  and  G  is  clamp  to  keep  the  arm  horizontal ;  a 
is  a  card  at  the  end  of  a  rod  for  the  near-test  of  inefficiency. 

The  prism  holder  or  slide  contains  two  cells,  in  each  of  which 
rotates  a  disc,  each  disc  carrying  a  prism  of  five  degrees.  Each  disc 
is  furnished  with  a  border  of  teeth  or  cogs.     A  small  gear  wheel 


TESTS    FOR    HETEROPHORIA. 


415 


placed  between  the  discs  communicates  movement  from  one  disc  to 
the  other.  Around  the  outer  part  of  the  border  of  each  cell  there  is 
a  narrow  band,  on  which  is  marked  a  scale  of  degrees,  increasing 
from  the  center  each  way  from  zero  to  eight  degrees,  the  numbers 
representing  the  refracting  angle  of  a  prism.  To  the  outer  side  of  this 
scale  there  is  an  equivalent  scale  of  prism  diopters.      The  prism 


holder  is  placed  upon  the  arm  of  the  phorometer  and  the  arm 
rendered  absolutely  horizontal  by  means  of  the  small  spirit  level 
attached  to  it.  The  side  of  the  slide  upon  which  the  scales  are 
marked  is  placed  away  from  the  patient.  The  edge  marked  R.  H. 
and  L.  H.  will  then  be  before  the  patient's  right  eye  and  that 
marked  Es.  and  Ex.  before  his  left.  To  determine  hyperphoria 
bring  the  handle  of  the  instrument  to  a  vertical  position.  The 
pointer  will  then  be  at  zero.  The  slide  should  be  about  six  inches 
in  front  of  the  patient's  eyes.  The  patient  now  looks  through 
the  two  prisms  at  a  card  hung  at  a  distance  of  twenty  feet,  across  the 
room,  upon  which  is  drawn  a  dot  and  crossed  lines  through  it,  thus : 


41 6  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

The  patient  sees  double  images  of  this  cross,  side  by  side.  The 
horizontal  line  is  made  long  enough  so  that  when  doubled  the  two 
horizontal  lines  butt  end  to  end,  enabling  the  patient  to  readily  tell 
whether  one  dot  is  higher  than  the  other  or  not.  If  one  image  is 
higher  than  the  other  we  ascertain  to  which  eye  that  image  belongs. 
Thus  the  prisms  are  now  before  the  eyes  with  their  bases  in,  there- 
fore, the  images  are  homonymous,  that  is  the  image  belonging  to  the 
right  eye  is  on  the  right  and  that  of  the  left  eye  on  the  left.  If  the 
right  image  is  higher  it  indicates  that  the  right  eye  has  a  weak 
superior  rectus  muscle,  and  the  trouble  is  called  left  hyperphoria  and 
vice  versa.  The  right  image  is  to  be  brought  down  to  the  level  of 
the  other  one,  when  the  scale  upon  the  outer  edge  of  the  disc  will 
indicate  the  amount  of  weakness. 

The  apex  of  the  right  prism  must  then  be  pulled  down,  by  pulling 
the  handle  to  th^  patient's  right  hand.  By  making  the  rotation 
slowly  more  inefficiency  will  be  revealed  than  if  the  rotation  is  made 
quickly.  To  ascertain  the  amount  of  esophoria  and  exophoria  bring 
the  handle  to  the  horizontal  position.  The  images  of  the  cross  will 
now  be  seen,  the  one  above  the  other,  the  prisms  being  before  the 
eyes,  the  one  with  the  apex  up  and  the  other  with  the  apex  down. 
The  vertical  lines  through  the  two  images  of  the  cross  should  now  be 
continuous  if  there  is  balance  between  the  laterally-acting  muscles. 
If  one  dot  is  not  exactly  over  the  other  the  amount  of  error  is  ascer- 
tained by  rotating  the  handle  until  they  are  exactly  over  each  other. 
The  lower  of  the  two  crosses  belongs  to  the  right  eye  and  if  it  is  to 
the  right  there  is  esophoria,  and  if  to  the  left  exophoria.  The  handle 
is  then  moved  so  that  the  pointer  will  move  in  the  direction  of  the 
esophoria  or  exophoria  as  the  case  may  require.  Trial  prisms  may 
be  graduated  after  the  same  manner  to  work  in  a  trial  frame,  as  the 
prisms  in  the  slide  of  the  Stevens  phorometer.  When  a  prism  is 
rotated  before  the  eye,  the  object  looked  at  through  the  prism  ap- 
pears to  describe  a  circle  following  the  apex  of  the  prism.  The  cir- 
cle that  the  object  appears  to  describe  is  a  projection  or  a  smaller 
circle  upon  the  eye's  retina  described  by  the  rays  of  light  that  pass 


TESTS    FOR    HETEROPHORIA.  417 

through  the  prism,  and  are  refracted  towards  the  base  of  the  prism. 
If  no  bending  of  the  Hght  took  place  as  the  light  passed  through  the 
prism,  no  such  appearance  would  take  place  by  the  rotation  of  the 
prism.  Usually  a  four-  or  six-degree  prism  is  graduated  for  use  in 
the  trial  frame. 

The  following  applies  to  a  graduation  of  a  six-degree  prism. 
Divide  a  horizontal  line  into  twelve  equal  parts.  With  this  line  as  a 
diameter  construct  a  circle  ;  from  each  of  the  subdivisions  of  the  line 
erect  a  perpendicular  ;  from  the  intersections  of  the  perpendiculars 
with  the  circumference  of  the  circle  draw  radii.  Lay  the  prism  to  be 
marked  upon  the  figure  thus  constructed,  with  its  axis  coinciding 
with  the  central  radius,  and  with  its  base  upon  the  diameter  of  the 
circle.  The  prism  is  now  marked  with  a  glass  cutter  over  each  ra- 
dius drawn.  The  intervals  correspond  to  one  half  degrees.  The 
prism  is  now  placed  in  the  trial  frame  with  its  base  down,  and  if 
diplopia  is  not  developed  another  prism  is  placed  before  the  other 
eye  with  its  base  in  the  opposite  direction.  The  graduated  prism  is 
then  rotated  to  the  right  or  to  the  left  until  one  light  is  seen  directly 
over  the  other  one.  The  amount  of  lateral  deviation  is  then  read  off 
by  counting  the  number  of  graduations  between  the  90-degree  mark 
upon  the  trial  frame  and  the  axis  of  the  prism.  In  testing  for  ver- 
tical deviations,  the  prisms  are  turned  so  that  the  two  lights  are  seen 
side  by  side,  that  is  with  bases  in. 

The  amount  of  hyperphoria  is  then  read  off  by  counting  the  num- 
ber of  graduations  between  the  180-degree  mark  upon  the  trial 
frame  and  the  axis  of  the  prism.  Dr.  Stevens  has  devised  another 
test,  which  is  easy  of  application  and  one  in  which  the  position  of  the 
patient's  head  has  no  influence.  A  convex  lens  say  about  a  13  D. 
S.  is  covered  except  at  its  optical  center,  where  a  circular  opening  of 
3  mm.  or  less  acts  as  a  stenopaic  opening,  preventing  the  adjust- 
ment of  the  lens  as  a  prism  and  sharply  circumscribing  the  light  area 
as  seen  through  the  opening.  A  flame  looked  at  through  this  open- 
ing appears  as  a  large  bright  circle  of  light,  in  the  center  of  which  is 
seen  the  natural  flame  when  the  other  eye  is  opened,  if  orthophoria 
27 


4i8 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


exist.  The  disc  of  light  may  be  colored  red  to  contrast  with  the 
color  of  the  flame.  If  the  candle  flame  is  below  the  center  of  the  disc 
of  light  and  seen  by  the  left  eye  there  is  present  right  hyperphoria ;  if  to 
the  right  of  the  center  of  the  disc  there  is  exophoria  and  if  to  the  right 
and  below,  a  combination  of  the  two  exists,  i.  e.,  right  hyper-exophoria. 


Heterophoria. 


A  convenient  method  of  testing  the  extra-ocular  muscles  is  as 
follows :  A  piece  of  black  cardboard  about  two  feet  square,  with 
a  central  round  opening  and  divided  by  equidistant  horizontal  and 
vertical  lines,  is  hung  before  a  window  or  argand  burner  so  that  the 
light  shines  through  the  central  opening.  A  Maddox  rod  is  placed 
before  one  eye  of  the  patient.  If  there  is  present  imbalance  of  the 
muscles  the  streak  of  light  seen  by  the  eye  before  which  the  Mad- 
dox rod  is  placed,  is  seen  to  run  to  one  side  or  the  other  of  the 
central  opening  as  seen  by  the  other  eye.  The  amount  of  error  can 
be  read  off  directly  by  noting  which  line  upon  the  card  the  streak  of 


TESTS   FOR   HETEROPHORIA. 


419 


light  overlaps.  The  lines  upon  the  card  should  be  separated  i  cm. 
for  every  meter's  distance  at  which  the  test  is  to  be  employed.  Thus 
for  6  m.  distance  the  lines  should  be  6  cm.  apart.  Maddox's  one- 
prism  test  and  Prentice's  test  also  enable  one  to  read  off  directly  the 
amount  of  exophoria  or  esophoria. 

The  former  test  consists  of  a  series  of  figures  beginning  at  zero  and 
extending  to  the  right  in  black  and  to  the  left  in  red  figures.  A 
prism  of  about  six  degrees  is  used  to  throw  the  vision  of  the  right 
eye  say  below  that  of  the  left.  The  arrow  which  divides  the  two  sets 
of  figures  then  points  to  the  one  indicating  the  amount  of  deviation. 
The  Prentice  test  is  about  the  same  save  the  chart  is  composed  of  a 
series  of  vertical  lines,  numbered  from  the  middle  to  the  right  in 
black  and  to  the  left  in  red  characters.  The  Wilson  and  Lewis 
phorometers  combine  many  of  the  above  tests  in  the  one  instrument. 
The  test  of  the  balance  of  the  muscles  when  the  eyes  are  adjusted 
for  the  usual  reading  point  should  also  be  made.  In  the  ideal  con- 
dition of  the  extra-ocular  muscles  there  will  appear  near  exophoria 
of  from  four  to  six  degrees.  A  card  with  a  dot  and  crossed  lines 
upon  it  is  held  at  the  reading  distance  and  the  phorometer  set  for 
four  degrees  of  exophoria.  The  patient  now  views  the  doubled 
image  of  the  dot  and  lines  which  should  in  the  normal  condition  be 
directly  over  each  other.  The  Maddox  doubling  prism  is  also  of 
value  in  testing  the  near  balance.  Any  sort  of  a  deviation  may  be 
recognized  by  its  aid.  The  eye  not  behind  the  prism  is  the  one  con- 
sidered under  the  test.  A  card  upon  which  there  is  a  dot  and  hori- 
zontal line  drawn  through  it  is  held  at  the  reading  distance.  With  a 
doubling  prism  before  one  eye  there  appears  three  dots  and  three 
horizontal  lines.  If  there  is  balance  of  the  muscles  the  three  lines 
are  parallel  and  the  three  dots  beneath  each  other.  If  the  middle 
dot  seen  by  the  right  eye  is  too  far  to  the  left  it  shows  exophoria, 
and  if  too  far  to  the  right  esophoria.  Nearer  the  upper  dot  than 
the  lower  one  bespeaks  left  hyperphoria,  and  if  nearer  the  lower  dot 
right  hyperphoria.  Being  above  and  to  the  right  indicates  left 
hyperphoria-esophoria  and  so  on. 


420  THE   EYE,    ITS    REFRACTION   AND    DISEASES. 

In  oblique  astigmatism,  according  to  Dr.  Savage,  there  is  fre- 
quently a  weakness  of  the  oblique  muscles.  In  oblique  astigmatism 
the  retinal  images  of  upright  objects  are  oblique,  as  proven  by 
photography,  and  for  the  eye  to  recognize  the  object  as  upright  in 
space  the  image  must  fall  upon  a  vertical  retinal  meridian.  The 
function  of  the  obliques  in  oblique  astigmatism  is  to  rotate  the  eye- 
balls so  that  this  occurs.  In  oblique  astigmatism  of  any  kind  when 
the  meridians  of  the  greatest  curvature  diverge  above  there  is  a  ne- 
cessity for  action  on  the  part  of  the  superior  oblique  muscles  in  order 
to  prevent  diplopia.  This  action  begins  early  in  childhood  and  con- 
tinues until  the  case  is  corrected  or  until  single  binocular  vision  is  lost. 

If  the  meridians  of  the  greatest  curvature  converge  above,  the 
images  of  all  objects  in  the  two  eyes  are  so  displaced  that  the  inferior 
obliques  are  called  into  action  to  prevent  diplopia.  In  oblique  astig- 
matism without  an  exception,  the  retinal  image  is  displaced  towards 
the  meridian  of  greatest  curvature,  which  in  hyperopic  astigmatism  is 
the  best  curvature,  and  meridian  of  myopia  in  myopic  and  mixed  astig- 
matism. When  the  astigmatic  meridians  are  vertical  and  horizontal 
the  ciliary  muscles  are  alone  called  upon  to  overcome  the  error. 
Weakness  of  the  superior  obliques  is  more  annoying  than  that  of  the 
inferior,  as  the  former  are  called  into  action  every  time  the  eyes  are 
turned  down  as  in  the  act  of  reading.  They  are  often  unequal  to 
their  task  and  give  rise  to  symptoms  of  asthenopia.  The  inefficiency 
of  the  oblique  muscles  is  detected  by  the  following  method  :  With  a 
Maddox  prism  before  the  right  eye  the  left  one  is  considered  under 
the  test.  The  patient  looks  at  a  dot  with  a  horizontal  line  drawn 
through  it  held  at  the  reading  distance.  If  the  obliques  are  normal 
in  their  action,  the  three  lines  seen  by  the  two  eyes  will  be  parallel, 
while  if  either  oblique  muscle  is  under-acting  the  middle  line  of  the 
three  will  be  seen  to  dip  towards  the  upper  or  the  lower  line  at  one 
end  or  the  other  according  to  the  muscle  involved.  If  the  right  ends 
of  the  middle  and  the  bottom  lines  converge,  while  the  left  ends 
diverge,  the  superior  oblique  of  the  left  eye  is  shown  to  be  in  a  state 
of  under-action. 


TESTS   FOR   HETEROPHORIA.  42 1 

Figure  II  represents  the  relation  of  the  lines  when  the  left  inferior 
oblique  muscle  is  too  weak. 

The  same  appearances  if  the  right  eye  was  under  the  test  would 
indicate  exacdy  the  opposite  condition  of  affairs, 
that  is  in  the  first  case,  inefficiency  of  the  in- 
ferior oblique  and  in  the  second,  inefficiency  of 
the  superior  obHque  muscle.  If  there  is  per- 
fect equilibrium  the  three  lines  will  be  parallel 

as  in  III. 

-• 

The  sort  of  diplopia  caused  by  oblique  astig-  " 

matism,  and  the  manner  in  which  rotation  of  the 

eyeballs  by  the  oblique  muscles  corrects  it,  is    • 

demonstrated  in  the  following  way :  , 

Place  a  —  3  D.  C.  before  each  eye  in  a  trial  '" 

frame.  The  concave  cylinder  creates  3  D.  of  hyperopic  astigmatism 
in  each  eye.  Place  the  axis  of  the  cylinder  before  the  left  eye  at  90 
degrees  and  that  of  the  right  eye  at  135  degrees.  Place  an  opaque 
disc  in  front  of  the  right  eye  and  a  doubling  prism  in  front  of  the  left. 
A  horizontal  arrow,  head  to  the  left,  drawn  upon  a  card  is  now  looked 
at  through  the  prism.  Two  arrows  parallel  to  each  other  are  seen. 
The  opaque  disc  should  now  be  removed  from  before  the  right  eye.  A 
third  arrow  then  appears  between  the  other  two  but  not  parallel  with 
them.  On  removing  the  doubling  prism  two  arrows  are  at  once  seen, 
and  in  a  few  seconds  they  begin  to  open  and  shut  like  a  pair  of  scis- 
sors, and  finally  they  merge  into  one.  This  occurs  when  the  eyes 
are  under  the  effect  of  atropine  so  that  the  correction  of  the  diplopia 
can  not  be  due  to  ciliary  muscle  action.  The  only  way  that  this 
phenomenon  can  be  explained  is  that  the  obliques  rotate  the  eyeballs 
until  the  two  meridians  of  retinal  stimulation  are  rendered  horizontal. 

Any  test  for  inefficiency  of  the  extra-ocular  muscles  is  not  to  be 
relied  upon  for  several  hours  after  a  mydriatic  or  cycloplegic  has  been 
instilled.  An  inefficiency  caused  by  a  refraction  error  is  called 
pseudo.  The  difference  between  the  apparent  weakness  of  muscle 
before  the  use  of  a  cycloplegic  (manifest  pseudo-inefficiency),  and 


422 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


that  discoverable  after  its  use  is  called  the  latent  pseudo-inefficiency, 
caused  by  the  latent  refraction  error  and  corrected  by  the  correction 

of  the  latter.  According-  to  the 
experiments  of  Guita  and  Bar- 
delli  it  would  seem  that  the  in- 
stillation of  cocaine  renders 
manifest  any  latent  muscular 
inefficiency.  The  manner  in 
which  this  agent  accomplishes 
this  result  is  not  clear. 

Before  adjusting  glasses  the 
amount  of  prism  adduction, 
abduction,  sursumduction  and 
deorsumduction  should  be  as- 
certained. For  it  will  at  times 
happen  that  when  the  other 
tests  show  a  balance  of  the 
muscles  that  the  adduction  or 
the  abduction  is  found  below 
par.  To  test  the  strength  of  a 
muscle  begin  with  a  prism  that 
the  eye  can  overcome.  The 
patient  regards  a  distant  candle 
flame  and  the  prism  is  placed 
before  the  eye  with  its  apex 
over  the  muscle  to  be  tested  or 
called  into  action.  Successively 
stronger  prisms  are  now  placed 
before  the  eye  in  the  same 
manner,  until  the  strongest  one 
is  ascertained  which  allows  of 
single  binocular  vision.  By  placing  successively  stronger  prisms 
before  the  eye  the  muscle  behind  the  apex  of  the  prism  is  gradually 
led  to  do  more  work  by  a  gradual  increase  in  the  amount  of  inner- 


TESTS   FOR   HETEROPHORIA.  423 

vation  sent  to  it — just  as  any  other  muscle  in  the  body.  Either  a 
Risley  prism  or  a  prism  pile  is  the  most  convenient  appliance  for  test- 
ing the  amount  of  prism  rotation.  The  Noyes  prism  pile  is  shown 
in  the  cut  on  page  422. 

This  set  is  made  up  of  three  prism  piles,  two  of  which  are  arranged 
so  as  to  furnish,  in  alternate  numbers,  all  degrees  from  i^°  to  22°. 
The  third  consists  of  two  superimposed  prisms  of  5°  and  10°  re- 
spectively, which  combined  produce  a  prism  of  1 5  °  in  the  center. 

The  power  of  adduction  is  tested  by  placing  the  apex  of  the  prism 
in,  of  abduction  by  placing  the  apex  of  prism  out ;  the  power  of 
elevation,  by  placing  the  apex  up,  and  the  power  of  depression, 
by  placing  apex  of  prism  down.  It  is  said  that  a  normal  external 
rectus  muscle  should  overcome  a  prism  of  8-10  degrees  and  an  in- 
ternal rectus  one  of  40-50  degrees,  and  the  vertical  recti  prisms  of 
2-5  degrees.  The  writer  is  convinced  that  the  amount  of  adduc- 
tion and  abduction  given  above  is  too  high,  adduction  seldom 
reaching  6  degrees  and  abduction  hardly  ever  over  30. 

If  there  is  a  paresis  of  the  abducens,  say,  of  the  one  eye,  the  prism 
adduction  of  that  eye  will  be  much  less  than  that  of  the  fellow  eye, 
but  it  will  now  and  then  happen  in  other  cases  that  the  adducting 
power  for  instance  will  be  found  to  be  a  few  degrees  greater  in  one  eye 
than  in  the  other,  caused  perhaps  by  the  one  eye  having  a  congeni- 
tally  inherently  stronger  muscle  than  its  fellow,  which  under  the  same 
amount  of  innervation  is  able  to  do  more  work.  In  such  cases  the 
treatment  of  the  heterophoria  should  be  unequally  divided  between 
the  two  eyes. 

A  good  converging  ability  may  be  absent  even  if  there  is  a  marked 
deviation  of  the  visual  lines  inward,  so  there  may  be  excessive  con- 
verging power,  when  exophoria  of  a  high  degree  is  manifest.  The 
fact  of  a  deficient  converging  power  with  esophoria  or  vice  versa  is 
indicative  of  anomalous  tension  in  the  vertically-acting  muscles,  in 
the  form  of  a  hyperphoria  or  a  tendency  for  both  visual  lines  to  rise 
above  or  to  fall  below  the  horizontal  plane,  namely :  anaphoria  or 
cataphoria.  The  absence  of  converging  power  should  warn  one  against 


424  THE   EYE.    ITS    REFRACTION   AND    DISEASES. 

the  assumption  that  he  is  dealing  with  a  simple  case  of  esophoria 
although  the  latter  is  shown  by  the  tests.  Similar  caution  should  be 
exercised  in  dealing  with  cases  of  apparent  exophoria  with  excessive 
degrees  of  convergence.  Anaphoria  and  cataphoria  are  only  diag- 
nosticated by  taking  the  fields  of  rotation  or  fixation,  or  by  measuring 
the  amount  of  prism  rotation  above  and  below  the  horizontal  plane.  In 
anaphoria  the  whole  field  will  be  found  to  be  moved  upwards  and  the 
superior  recti  stronger  than  the  inferior,  and  in  cataphoria  the  field  of 
fixation  is  dislocated  downwards,  and  the  inferior  recti  stronger  than 
the  superior.  Those  with  anaphoria  usually  look  straight  ahead 
from  under  the  brows,  that  is  with  chin  thrown  down  and  those  with 
cataphoria  look  straight  ahead,  with  head  thrown  well  back  during 
their  unconscious  moments. 

There  is  likewise  a  characteristic  position  of  the  head  in  cases  of 
hyperphoria,  that  is,  the  head  is  carried  on  the  side,  tilted  towards  one 
or  the  other  shoulder.  The  cause  of  the  tilting  of  the  head  is  a  com- 
plicating cyclophoria  so  often  found  in  cases  of  hyperphoria.  If  the 
complication  is  a  positive  cyclophoria  the  head  is  tilted  towards  the 
cyclophoric  side. 

Inefficiency  of  convergence  is  of  more  frequent  occurrence  than  is 
generally  supposed  and  is  found  chiefly  in  those  with  a  great  inter- 
pupillary  distance.  The  eyes  should  be  able  to  converge  upon  a 
point  at  3  in.  or  7.6  cm.  distance,  in  inefficiency  of  convergence  the 
c.  p.  may  be  removed  to  six  to  ten  inches.  The  prism  adduction 
may  or  may  not  be  found  to  be  below  par,  and  there  may  be  exo 
phoria  for  distance  or  muscle  balance,  but  it  is  the  rule  to  find  an 
abnormal  amount  of  exophoria  for  the  reading  distance  over  4°  to 
6°.  In  some  cases  the  inefficiency  of  convergence  is  so  great 
that  there  is  actually  a  paralysis  of  convergence,  while  each  eye 
can  adduct  to  its  normal  amount  in  associated  movements  with 
the  fellow  eye,  there  is  no  response  to  an  impulse  of  conver- 
gence. The  patient  may  overcome  the  effect  of  the  error  by  read- 
ing with  one  eye  closed,  thus  doing  away  with  the  need  of  conver- 
gence. 


TESTS   FOR   HETEROPHORIA. 


4^5 


Treatment. — The  treatment  of  pseudo-inefficiency  is  to  correct  the 
error  of  refraction.  Otherwise  to  develop  the  weak  muscle  or  mus- 
cles by  exercise,  or  to  relieve  them  of  their  work  by  prisms  in  form  of 
spectacles  worn  with  the  base  of  the  prism  over  the  weak  muscle — 
to  do  a  partial  tenotomy  on  the  stronger  muscle,  or  to  strengthen 
the  weaker  one  by  shortening  or  advancement,  or  by  some  similar 
operation. 

Allen  recommends  that  an  attempt  be  made  to  convert  the  phoria 
into  a  squint  by  daily  increasing  the  strength  of  the  prisms  used, 
their  bases  being  placed  over  the  weak  muscles,  and  then  to  relieve 
the  squint  or  cast  by  operation.  If  there  appears  an  esophoria  in 
hyperopia,  correct  the  total  hyperopia  save  .25  D.  to  allow  for  the 
return  of  the  ciliary  muscle  tone,  while  if  hyperopia  is  associated  with 
exophoria  correct  little  or  none  of  the  error,  but  try  to  develop  the 
internal  recti  muscles.  The  same  rules  apply  in  cases  of  hyperopia 
astigmatism.  Myopia  and  myopic  astigmatism,  on  the  other  hand,  is 
to  be  totally  corrected  when  associated  with  exophoria  and  only  par- 
tially so  when  associated  with  esophoria.  The  rationale  of  this  is  the 
association  between  convergence  and  accommodation.  The  greater 
the  call  upon  accommodation  the  greater  the  power  of  convergence, 
and  vice  versa. 

The  extra-ocular,  like  other  muscles,  can  be  developed  by  exer- 
cise. The  wearing  of  a  prism  with  its  apex  over  the  weak  muscle, 
the  strength  of  the  prism  being  a  little  less  than  that  required  to  pro- 
duce diplopia,  or  to  cause  the  eye  to  overcome  successive  strengths 
of  prisms,  a  change  to  a  stronger  prism  being  made  as  soon  as  the 
patient  overcomes  the  diplopia,  is  inferior  to  rhythmic  exercise.  Con- 
traction and  relaxation  short  of  fatigue  is  the  sort  of  exercise  that 
develops  a  muscle  anywhere  in  the  body.  The  internal  recti  muscles 
respond  to  exercise  much  more  perceptibly  than  do  the  externi. 
There  are  some  cases  in  all  classes  of  heterophoria  that  will  resist 
this  form  of  treatment.  Only  low  degrees  of  lateral  heterophoria, 
that  is  less  than  six  degrees,  can  be  converted  into  orthophoria  by 
exercise.     The  higher  degrees  can  only  be  overcome  by  converting 


426  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

them  into  squints  by  exercise  of  the  stronger  muscles  and  then  oper- 
ating, or  by  a  slight  tenotomy.  There  may  not  in  a  given  case  be 
established  balance  of  the  muscles  by  exercise  of  the  weaker  one  but 
the  patient  is  rendered  comfortable,  all  the  error  that  was  incom- 
patible with  comfortable  use  of  the  eyes  being  corrected.  Exophoria 
or  inefficiency  of  the  internal  recti  may  first  be  taken  for  study. 
There  are  two  methods  to  be  employed  by  either  of  which  the  muscles 
may  be  strengthened.  The  patient  looks  at  a  point  of  a  pencil  or  a 
small  lighted  taper  held  in  the  hand  at  arm's  length  in  the  median 
line  of  the  face.  While  regarding  the  object  it  is  made  to  approach 
the  eyes  slowly,  to  within  five  inches  of  the  latter.  Holding  it  there 
a  few  seconds,  the  patient  closes  his  eyes  for  a  moment  to  allow  the 
muscles  to  relax  and  then  repeats  the  same  procedure,  and  so  on 
until  the  eyes  begin  to  feel  weary.  These  sittings  are  repeated  two 
or  more  times  daily  for  weeks  or  months.  The  best  time  to  exercise 
is  in  the  morning  when  the  eyes  are  fresh  from  sleep.  The  second 
method  is  by  the  use  of  prisms,  bases  out.  The  strength  of  the 
prisms  used  is  from  one  to  eight  degrees.  One  should  be  placed 
before  each  eye.  The  treatment  begins  with  the  weaker  prisms,  and 
the  stronger  ones  brought  into  use  as  the  case  develops.  The  prisms 
are  worn  in  the  form  of  spectacles.  With  the  prisms  before  the  eyes 
the  patient  regards  the  flame  of  a  candle  at  twenty  feet  distance,  and 
then  raises  the  spectacles  from  his  eyes,  continuing  to  look  at  the 
candle  flame.  The  guiding  sensation  quickly  causes  the  eyes  to 
rotate  back  to  the  primary  position,  when  the  lenses  are  elevated, 
and  so  the  procedure  is  repeated. 

In  cases  where  exercise  fails  to  develop  the  power  of  convergence 
or  when  the  padent  can  not  be  treated  for  some  reason  by  that  method 
prisms  may  be  applied,  bases  in,  for  relief  of  the  asthenopia.  The 
strength  of  the  prisms  needed  is  ascertained  in  the  following  manner. 
A  card  with  a  small  dot  upon  it,  is  moved  closer  and  closer  towards 
the  eyes  of  the  patient,  in  the  median  line,  until  the  hmit  of  conver- 
gence upon  the  dot  is  reached.  This  fact  is  made  evident  by  the  dot 
appearing  double,  or  by  one  eye  of  the  patient  ceasing  to  fix  the  dot 


TESTS   FOR  HETEROPHORIA.  427 

and  wandering  towards  the  temple.  The  distance  of  C.  P.  is  then 
measured  in  centimeters  from  the  eye,  and  divided  into  100  cm.  to 
ascertain  the  number  of  meter  angles  of  convergence  in  use.  Sup- 
pose that  the  patient  ceases  to  converge  at  10  cm.  There  is  then  in 
use  10  m.  angles  of  convergence.  The  normal  function  equals  12.5 
meter  angles  of  convergence.  The  patient  then  lacks  2.5  m.  a.  to  be 
supplied  by  prisms.  Now  a  meter  angle  for  the  average  pupillary 
distance  equals  i°5o'  (for  each  eye),  therefore  2.5  m.a.  =  4.35  which 
is  practically  equal  to  a  4°  prism,  before  each  eye  with  the  base  in. 
The  prisms  are  to  be  worn  for  near  work  only.  Some  folks  are  un- 
able to  wear  any  but  the  very  weakest  prisms  on  account  of  the  dis- 
tortion produced  by  them  and  inability  to  properly  judge  distances 
for  the  first  few  days.  Under  these  conditions  the  correction  is  as 
follows  :  With  the  refraction  correction  on  have  the  patient  put  his 
attention  upon  a  dot  upon  a  card  held  at  the  distance  for  which  he 
wishes  to  use  his  eyes.  Beginning  with  the  weakest  prisms,  succes- 
sive strengths  are  placed  before  the  eyes  with  the  bases  in  until  the 
weakest  is  ascertained  with  which  there  is  no  redress  on  the  part  of 
the  eye  or  deviation  in  exclusion. 

There  is  but  one  method  to  develop  the  externi  and  that  is  by  the 
use  of  prisms.  The  prisms  used  must  not  exceed  four  degrees  in 
strength,  and  are  worn  before  the  eyes  with  their  bases  in,  and  as 
with  the  interni  a  distant  candle  flame  is  viewed  with  the  glasses  on 
and  then  they  are  raised  until  the  guiding  sensation  rotates  the  eyes 
back  into  the  primary  position,  which  has  occurred  as  soon  as  single 
binocular  vision  has  been  restored,  and  so  on.  Hyperphoria  is  like- 
wise only  susceptible  to  exercise  with  prisms.  The  strength  of  the 
prisms  should  vary  from  one  fourth  to  two  degrees.  The  base  of  the 
prism  should  be  down  before  the  eye  with  the  weak  superior  rectus 
and  the  base  of  the  other  up  before  the  fellow  eye,  that  is  the  base  of 
the  prism  before  the  eye  with  the  hyperphoria  should  be  up.  When 
there  is  a  general  weakness  of  the  ocular  muscles  unaccompanied  by 
a  general  debility  of  the  muscular  system  of  the  body,  there  will 
usually  appear  esophoria  for  distance  and  exophoria  for  near,  and 


428  THE   EYE.    ITS   REFRACTION   AND    DISEASES. 

neither  muscle  can  overcome  anything  Hke  the  strength  of  prism  that 
it  should.  To  relieve  either  the  esophoria  for  distance  or  the  exo- 
phoria  for  near  would  exaggerate  the  other  condition,  that  is  the  eso- 
phoria or  the  exophoria  as  the  case  may  be.  Both  the  externi  and 
the  interni  should  be  exercised  as  they  are  in  cases  of  uncomplicated 
esophoria  or  exophoria,  a  different  time  of  the  day  being  selected  for 
the  exercise  of  the  antagonizing  muscles.  General  tonics  also  are  to 
be  administered. 

Cyclophoria  or  inefficiency  of  the  obliques  is  to  be  corrected,  ac- 
cording to  Savage,  by  the  following  method :  The  treatment  is  by 
means  of  cyHndrical  lenses  so  placed  as  to  lead  the  guiding  sensation 
to  cause  contraction  of  the  weak  muscle.  A  plus  1.50  D.  C.  is  the 
most  useful  for  this  purpose.  One  is  placed  before  each  eye,  and  if 
the  superior  oblique  is  the  weak  muscle  the  axis  of  the  cylinder  is 
placed  in  the  lower  temporal  quadrant,  near  the  vertical  at  first,  say 
fifteen  degrees  therefrom,  and  the  inclination  of  the  axis  increased  as 
the  case  improves.  The  axes  of  the  cylinders  are  never  carried  be- 
yond 55  degrees,  however.  The  frames  are  raised  and  lowered  be- 
fore the  eyes  every  five  seconds  or  so  during  the  exercise.  In  ineffi- 
ciency of  the  inferior  obliques,  the  axes  of  the  cylinders  are  placed  in 
the  upper  temporal  quadrant,  near  the  vertical,  and  the  inclination 
of  the  axes  increased  as  the  case  improves.  Steele's  rule  in  cases 
of  oblique  hyperopic  astigmatism  is  :  In  those  cases  where  the  axes 
of  the  proper  cylinders  for  the  two  eyes  diverge  above,  place  the  cyl- 
inders, correcting  the  astigmatism,  at  the  points  which  will  give  the 
axes  the  greatest  divergence,  and  at  the  same  time  allow  of  the  best 
vision.  In  those  cases  in  which  the  axes  of  the  correcting  cylinders 
converge  above,  place  the  cylinders  so  that  their  axes  will  have  the 
greatest  amount  of  convergence  consistent  with  the  best  visual 
acuity.  There  is  such  a  condition  as  lateral  orthophoria,  in  which 
neither  the  internal  nor  the  external  recti  are  sufficiently  strong. 

Again  the  vertically-acting  muscles  may  be  in  balance,  but  in 
weakness.  On  the  other  hand,  the  balance  may  be  one  in  strength. 
Likewise  we  may  have  imbalance  in  weakness  or  in  strength.     We 


TESTS   FOR   HETEROPHORIA.  429 

speak  of  the  imbalance  in  weakness  as  asthenic  heterophoria  and  of 
the  imbalance  in  strength  as  sthenic  heterophoria.  Asthenic  hetero- 
phoria is  differentiated  by  the  fact  that  neither  of  the  antagonizing 
muscles  can  overcome  the  usual  strength  of  prism.  An  operation 
may  be  performed  for  sthenic  imbalance  in  the  form  of  a  tenotomy,  but 
for  the  relief  of  the  asthenic  form  an  advancement  operation,  if  any, 
is  to  be  done.  The  weaker  muscle  is  to  be  brought  up  to  the 
stronger  one,  and  then  an  attempt  made  to  develop  both  muscles  by 
certain  exercises.  Thus,  if  the  lateral  muscles  are  too  weak  the  pa- 
tient is  to  perform  what  is  called  the  wall-to-wall  evercise.  That  is : 
With  the  head  stationary  the  patient  is  to  look  alternately  from  one 
side  wall  of  the  room  to  the  other,  resting  now  and  then,  and  stop- 
ping the  moment  he  feels  fatigued.  If  the  vertically-acting  muscles 
are  at  fault,  the  ceiling-floor  exercise  is  used  to  develop  them.  The 
patient,  with  fixed  head,  first  looks  at  the  ceiling  and  then  at  the 
floor. 

TREATMENT   OF    SPASMODIC    ORTHOPHORIA   AND    REVERSED 
HETEROPHORIA. 

As  explained  in  a  former  chapter,  spasmodic  orthophoria  is  a  con- 
dition in  which  there  is  apparent  balance  between  the  extra-ocular 
muscles,  due  to  a  partial  spasm  of  the  weaker  antagonists,  while  re- 
versed heterophoria  is  that  condition  where  there  appears  an  eso- 
phoria,  for  instance,  due  to  a  spasm  of  the  internal  recti,  when  in 
reality  there  is  a  preponderance  of  inherent  strength  in  the  external 
recti  muscles.  In  all  cases  where  there  is  evidence  of  great  drain  of 
nervous  force,  and  when  correction  of  all  latent  refraction  errors,  and 
apparent  muscular  errors  fails  to  give  relief  of  symptoms,  one  should 
think  of  reversed  heterophoria  or  spasmodic  orthophoria.  Exophoria 
is  the  most  common  muscular  anomaly  found  in  spasmodic  ortho- 
phoria, and  may  be  suspected  when  there  is  distant  muscle  balance 
with  inefficiency  of  convergence.  This  condition  can  be  differentiated 
from  true  inefficiency  of  converging  power  in  the  following  manner  : 

Place  upon  the  patient  prisms  of  two  to  four  degrees,  or  a  strength 
just  short  of  diplopia,  bases  in,  and  allow  him  to  sit  awhile  in  the 


430  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

office  with  them  on.  If  there  is  a  concealed  heterophoria,  he  will, 
after  awhile,  be  able  to  overcome  stronger  prisms,  and  then  a 
slightly  stronger  pair  is  given  him  to  wear  home  and  to  keep  on 
constantly.  If  in  a  few  days  he  feels  much  better,  one  may  be  rea- 
sonably sure  of  the  diagnosis.  If  the  wearing  of  prisms,  bases  in,  in 
this  manner  aggravates  the  conditions,  the  diagnosis  is  at  fault.  It 
is  undoubtedly  a  fact  that  myopia  is  often  caused  to  increase  by  the 
excessive  tension  caused  by  a  concealed  or  reversed  heterophoria 
upon  the  eyeball. 

Reversed  heterophoria  should  be  thought  of  in  cases  of  hyper- 
opia with  exophoria  and  myopia  with  esophoria  and  the  treatment 
outlined  for  spasmodic  orthophoria  applied,  placing  the  bases  of  the 
prisms  over  the  weaker-acting  muscles.  After  all  the  muscular  error 
has  become  manifest,  or  as  much  of  it  as  can  be  developed  an  opera- 
tion is  performed  (tenotomy  or  advancement  as  outlined)  to  establish 
balance.  Slight  errors  are  corrected  by  exercise.  A  safe  line  to 
draw  between  operative  and  non-operative  cases  is  that  pointed  out 
by  Dr.  Savage,  which  is  :  If  diplopia  is  caused  by  placing  a  red  glass 
before  one  eye,  as  it  will  in  cases  that  threaten  to  pass  into  squints, 
one  should  operate,  and  if  not,  not.  Next  to  concealed  exophoria 
in  frequency  comes  concealed  hyperphoria.  A  hyfierphoria  may  be 
wholly  latent  to  diffusion  tests,  but  can  be  uncovered  in  the  following 
manner :  With  both  eyes  as  fully  corrected  as  far  as  the  plus  refrac- 
tion is  concerned,  place  before  the  right  eye  a  two-degree  prism  — 
base  down  and  if  the  patient  fuses  increase  the  strength  of  prism, 
until  diplopia  occurs,  then  record  the  result.  Remove  the  prism  and 
allow  the  right  superior  and  the  left  inferior  recti  to  relax  from  the 
strain  under  which  they  have  been  placed.  After  a  while  repeat  the 
same,  placing  the  base  of  the  prism  up  before  the  same  eye.  If  the 
eyes  will  fuse  under  stronger  prisms  when  the  base  of  the  prism  is 
down  before  the  right  eye,  there  is  right  hyperphoria  present,  and 
vice  versa.  The  subsequent  wearing  of  higher  prisms  will  demon- 
strate the  amount.  Spasmodic  orthophoria  and  reversed  hyperphoria 
can  only  be  determined  by  the  effect  produced  by  wearing  of  prisms. 


TESTS    FOR    HETEROPHORIA.  43 1 

Esophoria  is  seldom  latent  or  reversed,  but  often  spurious,  caused 
by  hyperopia  (pseudo-esophoria). 

Imbalance  of  the  extra-ocular  muscles  not  within  the  limits  of 
single  binocular  vision  will  be  dealt  with  under  the  head  of  strabis- 
mus. In  all  the  cases  considered  single  binocular  vision  is  not  only 
possible  but  habitual.  A  full  correction  of  heterophoria  should 
always  be  made  if  possible,  but  gradually,  that  is  the  strength  of  the 
prisms  worn  increased  every  several  weeks  until  the  total  error  is 
corrected.  The  more  sensitive  the  patient  the  weaker  must  be  the 
first  pair  of  prisms  worn  and  the  slighter  their  change  in  strength 
each  time. 

Before  leaving  the  subject  of  muscular  inefficiencies,  a  few  words 
must  be  said  about  the  stereoscope  as  a  means  of  detecting  and  cor- 
recting heterophorias.  If  the  half  pictures  of  the  stereoscope  are  at 
the  focal  distance  of  the  eye-piece,  and  the  refraction  error  of  the 
patient  corrected,  they  will  be  fused  if  they  are  separated  a  distance 
equal  to  the  pupillary  interval.  If  the  pictures  are  separated  a  dis- 
tance equal  to  the  pupillary  distance,  the  visual  lines  of  the  two  eyes 
need  only  to  be  parallel  to  bring  the  image  of  each  half  picture  upon 
symmetrical  portions  of  each  retina  so  that  when  the  images  are  pro- 
jected they  give  the  appearance  of  a  whole  stereoscopic  picture,  with 
its  characteristic  appearance  of  solidity  or  depth.  The  fused  stereo- 
scopic picture  appears  to  lie  midway  between  the  two  half  pictures. 
The  prisms  in  the  oculars  of  the  instruments  with  their  bases  out 
cause  the  image  from  each  half  picture  to  fall  upon  the  temporal  por- 
tion of  the  retina  of  the  corresponding  eye.  Each  eye  therefore  pro- 
jects its  image  nasally.  The  stereoscope  designed  by  Dr.  Derby 
enables  the  observer  to  secure  a  displacement  of  the  half  pic- 
tures in  both  the  lateral  and  vertical  senses.  The  background  of  the 
half  pictures  is  a  white  surface  upon  which  vertical  and  horizontal 
lines  are  engraved,  being  one  centimeter  apart  in  each  case.  The 
vertical  lines  are  numbered  right  and  left  from  the  middle  of  the  card. 
Experience  has  shown  that  the  measure  of  displacement  of  a  half 
picture  i  cm.  equals  a  prism  rotation  of  three  degrees.     In  front  of 


432 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


the  graduated  background  two  small  travelers  move.  Each,  like  the 
half  of  the  ordinary  trial  frame,  is  semicircular  and  graduated  from  o 
to  1 80  degrees.  In  these  travelers  the  half  pictures  are  placed,  the 
vertical  axis  of  the  pictures  being  at  90  degrees  for  an  ordinary 
anomaly  of  the  muscles.  The  half  pictures  may  be  moved  either  in 
a  lateral  or  vertical  sense,  and  their  position  determined  by  the  gradu- 
ated background.     The  distance  between  the  eye- piece  and  the  pic- 


tures can  be  altered  from  12  to  16  cm.,  the  normal  distance  being  14 
cm.,  the  focal  length  of  the  convex  prisms  of  the  oculars.  The  lenses 
are  7  D.  S.,  combined  with  five-degree  prisms,  bases  out.  The  dis- 
tance between  the  lenses  of  the  eye-piece  may  be  altered  to  suit  vary- 
ing pupillary  distances.  When  there  is  dynamic  equilibrium  the 
center  of  each  half  picture  will  be  ordinarily  3.5  cm.  from  the  middle 
line  (that  is  for  p.  d.  of  70  mm.),  and  centered  on  the  same  horizontal 


TESTS   FOR   HETEROPHORIA.  ^^2, 

line.     If  one  or  the  other  half  picture  has  to  be  moved  this  way  or 
that  in  order  that  the  two  may  be  fused  there  is  indicated  a  weakness 
of  the  muscle  of  the  eye  on  the  same  side  from  which  the  half  picture 
has  to  be  moved.     Thus  suppose  that  the  pictures  have  to  be  moved 
closer  together  than  70  mm.  before  the  observer  is  able  to  fuse  them. 
We  would  then   know  that  the  externi  were  under-acting.     Every 
centimeter  nearer  together  or  further  apart  the  half  pictures  are  placed 
causes  the  eyeballs  to  undergo  three  prism-degrees  of  rotation  to 
keep  the  pictures  fused.     By  placing  the  pictures  nearer  together 
than  the  pupillary  distance  the  internal  recti  are  caused  to  contract, 
the  muscles  relaxing  again  when  the  eyes  are  closed  or  when  the 
pictures  are  again  separated  the  distance  of  the  pupils  apart.     To 
call  the  external  recti  into  action  the  pictures  must  be  moved  apart. 
To  develop  any  muscle  with  the  stereoscope  the  half  picture  is  moved 
from  a  position  directly  in  front  of  the  eye  towards  the  muscle  to  be 
developed  and  after  keeping  it  at  the  extreme  point  of  fusion  for 
a  while  it  is  move  back  towards  the  primary  position  in  which  the 
visual  axes  were  parallel.     Usually  we  wish  to  strengthen  correspond- 
ing muscles  of  the  two  eyes  and  then  both  half  pictures  are  moved, 
thus,  for  developing  the  externi,  both  half  pictures  are  moved  out- 
wards until  fusion  is  no  longer  possible.     When  for  reason  the  ocu- 
lar muscles  fail  to  respond  to  exercise,  or  when  the  patient  cannot 
afford  to  do  without  the  use  of  his  eyes  while  they  growing  stronger, 
prisms  are  adjusted  in  trial  frames  in  such  a  manner  that  they  take 
the  strain  off  of  the  weak  muscles.     The  eyes  are  relieved  by  the 
prisms  of  maintaining  the  proper  position  for  single  binocular  vision  ; 
each  eye  rotating  in  a  position  of  rest  behind  the  prism,  thus  reliev- 
ing the  system  of  much  nervous  strain.     The  prisms  together,  one  for 
each  eye,  must  be  slightly  weaker  than  is  needed  to  render  the  case 
orthophoric  for  a  very  pronounced  change  is  not  well  borne.     Prisms 
stronger  than  four  degrees  can  seldom  be  worn  for  any  length  of  time 
with  any  degree  of  comfort,  as  objects  seen  through  them  appear  so 
distorted  that  the  confusion  arising  therefrom  is  greater  than  the  dis- 
comfort for  which  they  are  adjusted.     The  bases  of  the  prisms  must 


434  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

be  placed  over  the  muscles  to  be  relieved.  If  after  a  while  the  prisms 
cease  to  give  relief,  it  will  be  found  that  at  that  time  there  is  more 
manifest  heterophoria,  or  perhaps  an  actual  squint  has  developed. 
In  the  latter  case  a  first  class  tenotomy  is  done  and  in  the  former  a 
stronger  pair  of  prisms  adjusted.  The  hair-splitting  operations  (par- 
tial tenotomies)  done  for  the  relief  of  slight  heterophorias  are  to  be 
condemned,  as  they  seldom  establish  balance  and  if  too  much  cutting 
is  done  the  case  is  reversed,  that  is  an  esophoria  converted  into  an 
exophoria  or  vice  versa,  and  the  condition  is  as  bad  if  not  worse  than 
before.  The  other  operations  upon  the  muscles  such  as  tendon 
tucking  or  advancement  are  likewise  too  uncertain  to  be  of  much 
value  in  phoria  cases  except  those  that  threaten  to  pass  into  squints. 
It  is  much  better  to  convert  the  case  into  a  squint,  as  outlined  above, 
if  such  a  thing  will  come  to  pass,  and  if  not  the  constant  wearing  of 
prisms  or  exercise  will  relieve  the  symptoms  of  asthenopia. 


CHAPTER   XXVII 


APHAKIA 


Aphakia  means  the  absence  of  the  crystalline  lens  of  the  eye.  It 
is  rarely  congenital,  being  caused,  as  a  rule,  by  the  removal  of  the 
lens  for  cataract,  either  by  solution  or  by  extraction.  The  eyeball 
in  consequence  is  rendered  about  1 1  to  1 3  D,  hyperopic.  Any  pre- 
existing hyperopia  is  not  necessarily  increased  by  this  amount,  nor 
is  the  original  amount  of  myopia  always  diminished  to  the  same 
extent.  The  exact  amount  of  H.  in  the  aphakic  eyeball  may  be  cal- 
culated by  the  following  formula: 

F'lf  -\-F"lf"  =  \. 

From  the  values  of  the  simplified  eye  we  have,  /^  =  24  (anterior 
focal  distance  of  cornea),  F"  =  32  (posterior  focal  distance  of  cornea), 
and  y"  =  24.7  (posterior  focal  distance  of  eye),  giving  the  value  of 
/"'  =  — 81.2.  The  far-point  is  then  situated  81.2  mm.  behind  the 
apex  of  the  cornea.  This  ametropia  is  corrected  by  a  lens  of  96 
mm.  focal  length,  that  is,  a  10.4  D.  lens,  placed  at  15  mm.  in  front 
of  the  cornea.  To  ascertain  the  correcting  glass  for  aphakics  we  pro- 
ceed as  in  other  conditions  of  ametropia ;  we  can  not  find  the  refrac- 
tion of  the  eyeball  simply  by  diminishing  the  ante-operative  refraction 
by  1 1  D.  The  following  table  showing  the  relation  of  the  ante-  and 
post-operative  refraction  is  that  of  Dr.  Stradfelt. 


H. 

H. 

H. 

H. 

E. 

M. 

M. 

M. 

M. 

Before  operation. 

7 
H. 

H^ 

3 

H. 

I 

H. 

H. 

I 

H. 

H^. 

5 
H. 

7 

H 

After  operation. 

IS 

13-8 

I2.S 

"•3 

10.6 

10. 1 

8.9 

7.8 

6.6 

M. 

M. 

M. 

M. 

M. 

M. 

M. 

M. 

M. 

Before  operation. 

^. 

II 

H. 

13 
H. 

^H^. 

17 
H 

19 
H. 

21 
M. 

23 

M. 

25 

M. 

After  operation. 

S-5 

4.4 

3-4 

2.3 

1-3 

0.2 

0.8 

1.8 

2.7 

435 


436  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

In  general  after  the  extraction  of  the  crystaUine  lens  of  the  eye, 
one  divides  by  two  the  number  of  diopters  of  the  correcting  glass 
of  the  complete  eye,  and  when  concave  subtracts  it  from  ii,  and 
when  convex  adds  it  to  1 1  D.  to  ascertain  the  amount  of  refraction 
of  the  aphakic  eyeball. 

Let  us  call  the  correcting  lens  of  the  complete  eye  Z,  and  that  of 

the  resulting  aphakia  after  the  loss  of  the  crystalline  lens  L\  we  will 

then  have 

L  =  2{L'  —  \\)\  orZ  =  2Z'  — 22, 

22   +  Z  T  .  ^        T    I 

j^>  = ;  or  L'  =  11+ Lj  2. 

2 

The  length  of  an  eyeball  is  ascertained  by  the  formula 

F'  X  F" 
C" ^.derived  from  C'C"  =  /•'/•". 

C'  =  difference  between  the  first  conjugate  and  the  first  principal 
focal  points  =/'  —  F', 

y' =  distance  of  punctum  remotum  from  the  first  principal  point 
of  the  eye.  Accepting  the  measurements  of  the  schematic  eye  of 
Helmholtz  in  the  following  deductions,  if  the  correcting  lens  is  placed 
13  mm.  in  front  of  the  cornea,  it  is  situated  at  the  anterior  focus  of 
the  eye. 

f'  —  F'  =  the  focal  distance  of  the  correcting  lens. 

F'  =  15.5  mm.;  F"  —  20.7  mm. 

F'  y.  F"  —  2,21  mm.     If  the  correcting  glass  is  one  diopter,  then 

r>  J  ^„      F'XF"        321 

C  =  1,000  mm.  and  C "  = ^ = -£ —  =  .^21  mm."^ 

O  1,000       ^ 

That  is  if  the  correcting  lens  is  placed  at  the  anterior  focus  of  the 
complete  eye,  each  diopter  corresponds  to  a  difference  in  axial  length 
of  .321  mm. 

♦Measurements  of  Tscherning  give  :   ^    •  —  .353. 


APHAKIA. 


437 


There  is  a  source  of  error  in  the  examination  of  aphakics  as 
Dimmer  first  pointed  out,  due  to  the  fact  that  when  the  lenses  in  the 
trial  cases  are  combined  the  result  is  not  the  same  as  when  ground 
into  one  as  supplied  by  the  optician.  The  higher  strengths  of 
spherical  lenses  in  the  trial  cases  are  biconvex,  while  the  optician 
grinds  the  sphero-cylindrical  combination,  with  the  spherical  correc- 
tion on  one  side  of  the  glass  and  the  cylindrical  upon  the  other, 
which  is  placed  next  to  the  eye  whenever  the  cylinder  of  the  combi- 
nation is  weaker  than  the  sphere  if  convex  and  away  from  the  eye 
if  concave.  The  strongest  convex  or  the  weakest  concave  side  of 
the  lens  is  always  placed  away  from  the  eye.  The  optical  center  of 
a  biconvex  lens  is  situated  in  the  center  of  the  lens,  while  that  of  a 
plano-convex  lens  is  situated  at  the  apex  of  the  curved  side.  It  fol- 
lows that  the  spherical  effect  of  a  sphero-cylindrical  combination  is 
little  greater  than  that  of  a  biconvex  lens,  having  the  same  focal  dis- 
tance, the  posterior  focus  being  situated  a  little  nearer  the  lens  in 
the  former  case.  The  strong  lenses  of  the  trial  cases  should  be 
made  plano-convex,  to  overcome  this  possible  error.  The  distance 
at  which  the  sphero-cylindrical  lens  is  placed  in  front  of  the  eye 
exercises  an  influence  over  its  strength,  as  Ostwalt  first  pointed 
out. 

Suppose  that  the  eye  is  corrected  by  +  8  D.  S.  +  2  D.  C.  ax.  90° 
placed  at  15  mm.  in  front  of  the  cornea.  The  focal  distances  of 
such  a  glass  are  :  1,000/8  =  125  mm.  and  1,000/10=  100  mm.  The 
far-point  in  the  first  meridian  is  125  —  15  mm.  =  1 10  mm.,  and  in  the 
other,  100  —  15  =  85  mm. 

1,000/110  =  9  + D.,  and  1,000/8.5  =  II. 7  D. 

The  amount  of  astigmatism  is  then  11. 7  D.  -  9  D.  =  2.7  D.,  in- 
stead of  2  D.  This  makes  little  difference  in  the  subjective  exami- 
nation of  the  refraction,  as  the  lenses  from  the  trial  case  are  situated 
at  about  the  same  place  as  those  the  patient  will  wear  in  spectacles, 
but  this  is  not  the  case  with  ophthalmometry.     The  amount  of  error 


438  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

indicated  by  the  ophthalmometer  is  higher  than  the  lens  that  the 
patient  selects  signifies.  In  simple  cylindrics  the  same  influence 
makes  itself  felt  to  a  less  degree. 

The  absence  of  the  crystalline  lens  of  the  eye  is  detected  by  the 
absence  of  two  of  the  images  of  Purkinje.  The  aphakic  eyeball  is 
practically  devoid  of  all  accommodation,  and  a  +  3  D.S.  should  then 
be  added  to  the  distant  correction  for  reading.  A  +4  D.  S.  lens 
added  to  the  distant  correction  will  frequently  afford  better  new 
vision  than  a  +  3  D.  as  the  print  is  seen  more  magnified.  It  is  not 
advisable  to  add  any  stronger  lens  than  this,  as  then  the  reading 
point  will  lie  too  close  for  comfortable  use  of  the  eyes.  If  the 
patient  wishes  to  see  smaller  objects  than  this  affords,  at  closer 
range,  he  may  get  the  advantage  of  a  stronger  lens  by  moving  his 
spectacles  further  down  upon  his  nose.  Now  and  then  a  case  will 
be  seen  that  has  a  .certain  amount  of  accommodation  left,  due  per- 
haps to  a  bulging  forward  and  an  altered  form  of  the  anterior  sur- 
face of  the  vitreous,  brought  about  by  action  of  the  ciliary  muscle. 
Accommodation  would  then  be  favored  by  a  small  round  pupil,  and 
would  be  in  reverse  relation  to  the  thickness  of  the  posterior  capsule, 
and  take  place  only  when  there  is  a  marked  difference  in  the  index 
of  the  aqueous  and  vitreous,  as  is  often  the  cas6.  Schneller  claims 
that  the  accommodation  in  aphakic  eyeballs  is  due  to  elongation  of  the 
globe,  due  to  the  pressure  of  the  extra-ocular  muscles  when  the  eyes 
converge.  If  this  was  the  case,  the  eyeball  would  need  to  undergo  a 
lengthening  of  2,7  mm.  for  the  reading  distance.  Sadtler  pointed 
out  that  such  a  distention  is  impossible  from  the  nature  of  the  sclera. 
If  the  accommodation  was  due  to  an  alteration  in  the  curvature  of 
cornea  it  would  call  for  a  diminution  of  .5  mm.  in  fixing  an  object  at 
30  cm.  Keratoscopic  examination  shows  that  the  cornea  does  not 
alter  its  curvature. 

If  the  pupil  is  very  small  and  round  and  the  posterior  capsule  thin, 
there  is  enough  accommodation  at  times  preserved,  so  that  the  pa- 
tient can  use  the  same  lens  for  distant  and  near  seeing,  as  was  seen 
recently  in  a  case  that  came  under  the  writer's  notice. 


APHAKIA.  ^.g 

Inasmuch  as  the  optician  always  places  the  cylindrical  surface  of  a 
compound  lens  next  to  the  eye  of  the  patient,  whenever  the  cylinder 
is  weaker  than  the  combined  sphere,  the  examiner  in  testing  should 
place  the  cylinder  behind  the  sphere  in  the  trial  frame,  especially  in 
correcting  aphakia,  and  in  the  higher  degrees  of  ametropia.  The 
sphero-toric  lens  possesses  many  advantages  over  its  sphero-cylin- 
drical equivalent  in  the  correction  of  astigmatism,  and  especially  in 
aphakia.  As  described  in  a  former  section  a  toric  lens  is  a  section 
of  a  tore,  which  is  represented  by  a  watch,  with  its  sharp  curve  in 
one  direction  and  long  curve  in  the  other,  upon  its  edge.  Take  a  slice 
off  the  side  of  a  similarly  shaped  piece  of  glass,  and  we  have  a  toric  lens. 
Besides  the  serious  error  that  results  from  the  optician  substituting  a 
lens,  which  involves  a  change  in  the  position  of  the  nodal  points, 
sphero-cylindricals  give  rise  to  unpleasant  phenomena  due  to  inter- 
nal reflection  taking  place  between  the  surfaces  of  the  lens.  The 
patient  is  compelled  to  look,  as  it  were,  through  a  self-luminous 
medium,  the  reason  why  most  folks  can  not  see  as  well  in  feeble  and 
by  artificial  light  with  their  glasses  as  without  them.  Frequently  the 
test  lenses  will  give  a  patient  normal  vision,  while  the  sphero-cylin- 
drical equivalent  supplied  by  the  optician  does  not  allow  of  more  thao 
two  thirds  or  three  fourths  of  the  normal,  on  account  of  the  high 
degree  of  aberration  and  internal  reflection  in  such  lenses.  It  oc- 
curred to  Mr.  Prentice  that  the  internal  reflection  of  the  lens  could 
be  much  lessened  by  constructing  the  lens  with  less  curve  upon  its 
anterior  surface  ;  therefore  a  lens  having  a  toric  surface  upon  one 
side  and  a  spherical  surface  upon  the  other  was  suggested.  Such 
lenses,  although  expensive,  give  comfort,  and  are  extremely  light  in 
comparison  with  their  sphero-cylindrical  equivalents,  as  they  can  be 
made  much  thinner. 

In  aphakia  in  which  the  cornea  represents  the  only  refracting  sur- 
face, the  length  of  the  eye  is  identical  with  the  posterior  conjugate 
focal  distance  /"",  therefore  we  have 


440  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

According  to   Helmholtz  we   put   /  the  length  of  the  normal  eye 
=  23.8  mm. 


-R  =  punctum  remotum. 
0'  =r  anterior  focal  point. 
0''' =  posterior    "        " 
/''  =  anterior     '*    distance. 
^'' =  posterior    "  " 


We  must  now  calculate  the  anterior  conjugate  focal  distance  cor- 
responding to  /"",  which  we  do  by  the  following  formula  : 


which  is  derived  from 


/"  X  F' 


F'lf'  +  F"lf"  =  i. 


F'  =  23.26  mm.,  the  anterior  principal  focal  interval  of  the  aphakic  eye. 
F"=  2i^  mm.,  the  posterior  principal  focal  distance  of  the  aphakic  eye. 
If  the  correcting  glass  is  placed  13  mm.  in  front  of  the  cornea  then 
its  focal  length  must  be 

y  =t  1 3  mm. 

In  the  reduced  eye  in  which  the  cornea  is  the  only  refracting  surface, 
an  axial  length  of  23  +  mm.  represents  43.4  D.  of  refraction.  Taking 
the  strength  of  the  lens  of  the  eye  to  be  11  D.,  we  reduce  the  re- 
fracting power  of  the  eye  to  the  same  extent,  for  the  removal  of  the 
lens.  This  would  leave  the  eye  43  —  11  D.  =  32  D.  refractive,  which 
corresponds  to  a  focal  interval  of  3 1  +  mm. 

To  Calculate  the  Refraction  of  the  Complete  Eye  from  the  Known 
Refraction  of  an  Aphakic  Eye. — /"  is  the  quantity  sought,  f\  F'  and 
F"  being  known.     If  an  8  D.  S.  lens  is  needed  at  1 3  mm.  in  front  of 


APHAKIA. 


441 


the  cornea  to  correct  the  ametropia  produced  by  removal  of  the  crys- 
talline lens,  what  was  the  original  refraction  of  the  eye  ? 

f'-F'' 


R  —  Punctum  Remotum 

^'  -  Ant.  Focal  Point 

^"—  Post     .. 

H   —  First  Principal  Point 

F'  —  Ant.  Focal  Distance 

F"—  Post      .. 


f'  is  negative  in  value  as  the  first  conjugate  focus  lies  behind  the  eye- 
ball, the  refraction  being  hyperopic,  at  a  distance  of  125  —  13  mm. 

=  112  mm. 

/8)iooo        \ 


Therefore 


125  mm. 


.   _/'  X  F"  _    112X31     ^ 


/"  = 


f'  +  F'      1124-23.26 


25.6  mm. 


Inasmuch  as  the  eye  was  longer  than  the  normal  one  (23.8  mm.), 
the  refraction  was  originally  myopic,  and  inasmuch  as  each  3  D.  of 
refraction  corresponds  to  a  difference  in  axial  length  of  i  mm.,  the 
difference  between  the  length  of  this  eye  and  the  normal  eye  indi- 
cates that  the  eye  with  its  own  lens  needed  in  addition  one  of  —  5.3 
D   S.     To  simplify  this  for  practical  use,  let  us  consider  the  formula 


C"  = 


F'  y^F' 


m 


which  C"  =  the  difference  in  Ifength  between  the  normal  and  the 


442  THE   EYE,    ITS   REFRACTION   AND    DISEASES. 

ametropic  eye,  and  C  =  the  focal  interval  of  the  lens  placed  at  the 
anterior  principal  focal  point  of  the  eye.     Its  value  is 

^  C 

If  we  make  C"  =  i  mm.,  C  =  F' X  F" . 

In  the  complete  eye  /^'  X  /^"  =  32 1  mm.     Therefore 

\\  C  =  1,000/321  mm.  =  about  3  D. 

In  the  aphakic  eyeball,  F'  X  F"  =  721  mm.     Therefore 

ifC'  =  ~ =  about  1.4  D. 

'  721 

One  millimeter's  difference  in  length  of  the  normal  eye  equals 
about  3  D.  difference  of  refraction,  while  in  the  aphakic  eyeball  only 
a  difference  of  1.5  D.  A  difference  of  i  D.  in  the  correcting  glass 
in  aphakia  indicates  double  the  difference  of  length  that  it  does  in 
the  complete  eye,  or  a  i  D.  lens  has  twice  the  influence  over  the 
complete  eye  that  it  does  over  the  aphakic  eye.  The  above  values 
are  not  exact  since  slightly  different  results  are  obtained  according  to 
the  measurements  accepted  for  the  normal  complete  eye. 

The  aphakial  eyeball  does  not  appreciate  the  difference  in  strength 
between  two  lenses  unless  it  is  equal  to  one  diopter,  because,  as 
pointed  out,  a  one-diopter  lens  has  twice  the  influence  over  the  refrac- 
tion of  the  complete  that  it  has  over  the  refraction  of  the  aphakial  eye- 
ball. After  cataract  extraction,  as  well  as  after  iridectomies  and  other 
operations  upon  the  cornea,  there  is  a  flattening  of  the  corneal  curve 
at  right  angles  to  the  direction  of  the  corneal  section.  After  cataract 
operation  this  gives  rise  to  several  diopters  of  astigmatism  against 
the  rule,  usually  corrected  by  a  one,  two  or  three  plus  cylindrical  lens 
with  its  axis  transverse.  For  several  months  after  the  operation,  the 
amount  of  astigmatism  undergoes  a  change  due  to  the  contraction  of 
the  wound  cicatrix  at  first,  and  finally  to  the  cornea  establishing  its 
rotundity  to  a  certain  degree.  In  a  few  cases  we  find  a  high  degree 
of  corneal  astigmatism  with  the  rule  after  a  cataract  operation. 


CHAPTER  XXVIII 


SPECTACLE,   NOSE-GLASS  FITTING,   MEASURING  LENSES,  ETC. 

To  accurately  fit  a  pair  of  spectacles,  the  following  measurements 
must  be  taken.  The  distance  between  the  pupils,  the  distance  be- 
tween the  temples  ;  the  distance  from  the  tips  of  the  lashes  to  behind 
the  ear  on  a  line  with  the  epitragus ;  the  height  of  the  nose  ;  the 

width  of  the   nose  at 
base  ;    and  the  depth 
of  the  nose  or  the  dis- 
tance between  the  ends 
of  the  lashes  and  the 
crest  of  the  nose.    The 
pupillary     distance    is 
obtained  by  means  of  one  of  the  many 
pupillometers  on  the  market,  or  by  a 
rule  held  over  the  bridge  of  the  nose. 
The  pupillometer  shown  in  the  cut  is  a 
most  convenient  one.    The  instrument 
is,  as  shown,  placed  upon  the  bridge  of 
the  nose,  and  the  thumb-screw  moved 
backward  and  forward  until  the  two 
pointers  are  directly  centered  upon  the 
pupils.     The  distance  is  then  read  in 
mm.  from  one  side,  or  in  inches  from 
the  other,  as   one  desires.     The  op- 
tical centers  of  the  spectacle  lenses  must  be  this  distance  apart. 

Maddox  suggests  that  the  interaxial  distance  instead  of  the  inter- 
pupillary  distance  be  taken  to  get  the  lenses  properly  centered 
before  the  eyes,  for  there  are  a  few  cases  that  have  decidedly  eccen 

443 


444 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


trically  placed  pupils  and  others  have  abnormally  large  angles  alpha. 
The  distance  between  corresponding  parts  of  the  reflected  image  of 
a  window  or  other  object  from  the  cornea  of  each  eye  is  measured, 
or,  better  still,  light  is  thrown  into  the  eyes  from  an  ophthalmoscopic 
mirror,  the  central  hole  of  which  the  patient  fixes.  The  distance 
between  the  catoptric  images  is  then  measured. 

If  the  lenses  are  not  properly  centered  they  have  a  prismatic  effect. 
At  times  we  desire  to  decenter  the  lenses  in  their  rims,  in  cases  of 
heterophoria,  to  relieve  the  strain  upon  the  weak  muscles.  If  the 
lenses  are  convex  and  decentered  inwards  the  effect  is  that  of 
prisms  with  bases  in,  each  of  a  strength  (in  prism-diopters)  equal  to 
the  strength  of  the  lens  multiplied  by  the  number  of  centimeters  it 
is  decentered.  If  convex  spectacle  lenses  are  decentered  outwards 
the  effect  is  that  of  a  pair  of  prisms  with  bases  out.  It  is  just  the 
reverse  with  concave  lenses.  Vertical  decentration  of  lenses  also 
produces  a  prismatic  effect.  In  the  majority  of  cases  the  distance 
between  the  temples  is  regulated  by  the  pupillary  distance,  but  some 
cases  require  an  unusual  width  between  the  temples,  owing  to  an 
extreme  fullness  of  the  patient's  face.  It  is  desirable  to  take  this 
measurement  separately  so  that  the  temple  pieces  do  not  cut  into 
the  sides  of  the  face.  This  distance  may  be  taken  by  aid  of  a  rule, 
or,  better,  take  a  spectacle  frame  that  is  comfortable  and  measure 
the  distances  between  the  temple  pieces  one  inch  behind  the  lenses. 
The  height  of  the  nose  is  necessary  to  determine  the  depth  of  the 

nose-piece  of  the  spectacles  to 
be  furnished.      It  is  obtained 
by  drawing  an  imaginary  line 
across  the  face  on  level  with 
the  pupils,  and  measuring  from 
the  point  where  it  intersects  the 
bridge  of  the  nose  to  the  crest 
or  root  of  the  nose  (Fig.  i).     This  determines  the  height  of  the  nose- 
piece  for  spectacles  for  distance  or  constant  wear.      It  brings  the 
lenses  well  up  in  front  of  the  eyes  (Fig.  2).     The  centers  of  the  read- 


FlG.    I. 


SPECTACLE,    NOSE-GLASS    FITTING,    MEASURING    LENSES.  445 

ing  lenses  should  be  a  bit  nearer  together  and  slightly  lower  than 
for  distant  use.  The  distance  between  centers  is  made  1/16  to  1/8 
inch  less  and  the  saddle  1/16  to  1/8  inch  deeper  (Fig.  3). 

Reading  glasses  should  be 
tilted  out  at  the  top,  as  shown 
in  Fig.  3,  so  that  their  plane 
is  parallel  to  that  of  the 
reading  matter.  Looking 
obliquely  through  the  lenses 
if  they  are  set  vertically 
before  the   eyes   imparts  to 

Fig,  2.  Fig    ■? 

them  a  cylindrical  effect,  ren- 
dering the  glasses  less  comfortable  than  they  should  be  and  giving 
rise  perhaps  to  eye-strain. 

The  cylindrical  effect  produced  by  looking  obliquely  through  a 
spherical  lens  is  demonstrated  by  viewing  a  square  through  a  strong 
convex  or  concave  sphere  held  slantingly  before  the  eye.  The  square 
no  longer  appears  square  but  as  a  parallelogram,  longer  than  it  is 
broad,  or  vice  versa,  according  to  the  position  of  the  lens.  Lenses 
that  are  worn  constantly  should  be  slightly  tilted  out  at  the  top  but 
to  a  less  degree  than  those  used  only  for  near  vision.  The  width  of 
the  nose  is  taken  at  two  points,  namely,  at  the  crest  and  at  the  base. 
These  measurements  may  be  taken  by  sighting  the  nose  over  a 
graduated  rule  or  by  means  of  a  pair  of  calipers. 

Good  results  are  obtained  by  shaping  a  piece  of  lead  wire  across 
the  bridge  of  the  nose,  and  then  measuring  the  wire  curve.  The 
depth  of  the  nose  regulates  the  distance  of  the  bridge  of  the  specta- 
cles in  front  of  or  behind  the  plane  of  the  lenses,  and  is  according  to 
the  prominence  of  the  patient's  nose,  or  eyes  or  length  of  eyelashes. 
This  measurement  may  be  taken  by  holding  a  piece  of  cardboard  as 
near  to  the  eyes  as  the  sweep  of  the  lashes  will  permit,  and  then 
measuring  the  distance  between  the  card  and  the  crest  of  the  nose. 
The  contour  of  the  nose  is  best  fitted  with  a  saddle  bridge  which  has 
superseded  all  other  kinds  of  spectacle  bridges.     By  lengthening  or 


446  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

shortening  the  shanks  of  the  saddle  bridge,  the  lenses  are  made  to 
occupy  the  desired  position  in  front  of  the  eyes.  When  the  eyes  are 
prominent  and  the  nose  flat,  the  saddle  is  ordered  back  of  the  frame, 
and  when  the  nose  is  prominent  and  the  eyes  receding,  the  bridge  is 
ordered  in  front  of  frame.     It  is  spoken  of  as  being  on  line  when  the 


HEYROWITZ.  anW^     MErHOWlTl. 


edge  of  the  bridge  lies  in  the  plane  of  the  lenses.  The  two  figures 
show  the  saddle  in  front  of  and  back  of  frame. 

By  far  the  best  method  of  measuring  for  spectaclp  frames  is  to 
have  a  number  of  assorted  trial  spectacle  frames.  From  one,  the  set 
of  the  bridge  may  then  be  ascertained,  and  from  another  the  width 
of  temples  and  so  on.  By  putting  the  measurements  thus  gotten 
together  a  well-fitting  pair  of  spectacles  is  obtained.  When  a  trial 
frame  is  found  to  fit  the  patient,  its  measurements  may  be  ascertained 
by  aid  of  Well's  frame  measure,  or  by  aid  of  the  rule  shown  in  the 
cut  on  next  page.     The  latter  answers  all  purposes. 

On  one  side  of  the  rule  the  measurements  are  taken  in  inches,  and 
on  the  other  in  millimeters,  the  frame  to  be  measured  is  laid  down 
upon  the  rule  with  the  right  lens  coinciding  with  one  of  the  ellipses 
at  the  end  of  rule,  according  to  the  size  of  the  glass.  The  pupillary 
distance  is  then  noted  at  the  point  where  the  nasal  edge  of  the  other 
lens  is  in  contact  with  the  rule.  The  width  of  the  saddle  at  base  is 
obtained  by  placing  it  upon  the  tapering  end  of  the  rule,  and  the 


SPECTACLE.    NOSE-GLASS   FITTING,    MEASURING   LENSES.  447 


temple  distance  ascertained  by  placing  the  rule 
between  the  temple  pieces  and  noting  the  dis- 
tance upon  the  rule  at  the  place  marked 
"temple  distance." 

The  instrument  shown  on  next  page  is  de- 
signed to  facilitate  taking  the  various  measure- 
ments of  spectacle  frames.  The  scale  is  made 
from  spring  tempered  steel,  the  graduations  en- 
graved in  the  best  manner,  and  the  metal  parts 
finely  nickel  plated. 

All  measurements  of  any  style  frame  can  be 
readily  determined  either  in  millimeters  or  in- 
ches, including  height,  inclination  and  base  of 
nose-piece,  pupillary  distance,  etc.,  and  by  the 
graduation  on  the  reverse  side  of  the  largest 
scale  the  distance  between  temples,  length  of 
temples,  etc.,  can  be  obtained.  The  instrument 
can  also  be  used  as  a  pupillometer. 

If  it  is  desired  that  the  one  pair  of  spectacles 
answer  for  both  near  and  distant  seeing,  when 
the  patient  requires  a  different  strength  for  each, 
the  reading  glass  is  added  to  the  distance  one 
in  the  form  of  a  segrment  or  lenticular.  Such 
lenses  are  called  bifocals.  The  split  bifocal  is 
made  of  two  separately  ground  lenses  set  edge 
to  edge,  This  is  the  oldest  form  of  bifocal  and 
is  called  the  Franklin  lens.  The  cemented  bi- 
focal is  made  by  cementing  upon  the  distant  lens 
a  piece  from  the  edge  of  the  lens  needed  in 
addition  for  near  seeing.  The  solid  or  whole 
bifocal,  which  is  little  used  on  account  of  its 
prismatic  effect,  is  made  by  grinding  off  of  the 
upper  third  of  the  lens  that  is  proper  for  near 
seeing  sufficient  to  make  it  the  proper  distant 


O 


V-fe 


3/4 


'^b 


'/8 


'5/tb 


Tn 


oiP  $^  ^ri^o^ 


i^; 


448 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


correction.  There  are  a  few  people  that  never  can  get  accustomed 
to  lenticulars.  They  are  continually  trying  to  see  the  floor  in  going 
up  and  down  stairs  or  what  not  through  the  strong  lower  part  of  the 
glass  or  confused  by  seeing  the  edge  of  the  lenticular,  or  on  account 
of  an  anaphoria  are  unable  to  properly  direct  their  eyes  downward. 


Well's  Frame  Measure. 

Such  must  have  two  pairs  of  glasses,  one  for  distance  and  the  other 
for  near  work.  Instead  of  the  two  pairs,  necessitating  the  taking  of 
one  pair  off  and  putting  the  other  on  every  time  the  patient  wants 
to  read  or  sew,  a  pair  of  fronts,  or  spectacles  without  the  temple 
pieces,  but  small  hooks  to  fasten  over  the  distant  correction  may  be 
used.  Fronts  most  always  give  satisfaction  but  the  lenses  of  the 
spectacles  over  which  they  are  worn  soon  become  scratched  from 
their  use.  Half  fronts,  those  cut  away  above,  may  be  used  if  the 
person  needs  to  glance  up  frequently  from  his  work  to  look  at  a 
distance. 

For   nose-glasses   there   are   only   three    measurements   needed, 
namely,  the  pupillary  distance  and  the  width  of  the  nose  at  crest 


SPECTACLE,    NOSE-GLASS   FITTING,    MEASURING   LENSES.         449 

and  base.  The  latter  two  measurements  are  necessary  to  ascertain 
how  far  apart  the  clips  or  guards  must  be  so  that  when  the  glasses 
are  upon  the  nose  the  lenses  will  stand  horizontally.  For  those  with 
astigmatism,  especially  of  a  high  degree,  it  is  better  to  prescribe 
spectacles  unless  the  person  is  careful  to  note  when  the  glasses  fail 
to  set  horizontally  and  reports  to  have  them  straightened  up.  With 
the  introduction  of  offset  clips  many  of  the  difficulties  of  fitting  nose- 
glasses  were  overcome.     Figure  i  shows  the  old  form  of  regular  clip, 


Fig.  I. 
which  is  not  now  used  save  for  reading  glasses  with  simple  spheres. 
Figure  2  shows  the  offset  clip. 


Fig.  2. 


The  best  way  to  get  measurements  between  the  clips  above  (nose 
at  crest)  and  below  (nose  at  base)  is  to  place  upon  the  padent's  nose 
29 


450 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


a  pair  of  offset  clip  nose-glasses,  placing  them  in  the  proper  position 
upon  the  nose  —  that  is  where  they  seem  to  hold  firmly  and  feel  com- 
fortable, and  then  mark  with  ink  and  pen  a  horizontal  line  across 
each  lens,  bisecting  the  pupils.  The  glasses  are  then  taken  off  and 
held  so  that  the  two  horizontal  lines  will  form  a  continuous  line  and 
the  distance  between  the  clips  above  and  below  measured  with  the 
rule.  One  pair  of  old  nose-glasses  will  do  for  all  measurements 
between  clips  (see  figure).     When  the  glasses  are  taken  off  the  dis- 


tances c  and  d  are  measured,  while  lines  6"  are  held  horizontally. 

The  proper  P.  D,  is  obtained  by 
altering  the  size  of  the  lenses,  or 
by  means  of  extended  posts.  Posts 
are  made  in  graduated  lengths  from 

0  to  4,  the  length  increasing  one  six- 
teenth of  an  inch  with  each  number. 
They  are  especially  useful  when  the 
distance  from  the  crest  of  the  nose 
is  greater  on  one  side  than  oh  the 
other,  making  it  necessary  for  the 
center  of  one  lens  to  be  further 
from  the  nose  than  the  other. 
Whenever  possible,  order  post  No. 

1  and  alter  the  size  of  lens  to  cor- 
respond as  a  more  satisfactory  fit  is  obtained  when  the  glasses  set 


SPECTACLE,    NOSE-GLASS   FITTING,    MEASURING   LENSES.         451 

close  to  the  side  of  the  nose,  being  more  or  less  top-heavy  when 
extended  posts  are  used. 

If  a  receding  bridge  of  nose  is  accompanied  by  long  lashes,  we  use 
the  set-back  post,  or  a  clip  with  an  extra  long  shank.  The  set-back 
post  accomplishes  for  eye-glasses 
what  the  saddle  bridge  does  for 
spectacles.  The  set-back  posts 
carry  the  lenses  one  eighth  inch 
further  forward,  from  the  usual 
position,  on  plane  with  the  lenses. 
The  posts  can  be  reversed,  carry- 
ing the  lenses  backward  for  cases 
with  prominent  noses  and  reced- 
ing eyes.  They  may  also  be  com- 
bined with  the  extended  posts. 

If  the  patient  has  a  very  promi- 
nent brow,  it  is  advisable  to  have  the  spring  of  the  nose-glasses  tilted 
forward  as  shown  in  the  cut.  This  form  of  spring  is  known  as  the 
Grecian  spring.  If,  on  account  of  the  shape  of  the 
patient's  nose,  the  lenses  in  the  usual  position  set  too 
high  up,  or  if  the  glasses  are  to  be  used  only  for  read- 
ing, the  lenses  can  be  lowered  by  altering  the  position 
of  the  posts  on  the  frame  or  lenses  at  the  point  of 
their  attachment.  The  figure  below  shows  the  regular 
manner  of  attaching  the  posts  on  the  center  line  and 
the  so-called  C.  D.  No.  2  position,  in  which  the  posts 
are  set  one  eighth  of  an  inch  above  it.  By  combination 
of  extended  posts,  set-backs,  tilted  spring,  C.  D.  No.  2 
position,  and  so  forth,  with  malleable  pivot  clips,  which 
Grecian  or  can  easily  be  bent  to  the  proper  shape,  almost  any 
iLTED  pRiNG.  ^^^  ^^^  ^^  fittcd  wlth  3.  pair  of  eye-glasses. 
The  oculist  should  always  examine  his  patient's  glasses  to  see  if 
they  are  as  ordered.  The  fit  should  be  carefully  looked  after  and 
then  the  lenses  examined.     A  convex  spherical  lens  is  recognized  by 


MErnowirjL 


452 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


the  fact  that  when  an  object  is  looked  at  through  the  lens  and  the 
lens  moved  from  side  to  side  or  backward  and  forward,  the  object 
appears  to  move  in  a  direction  contrary  to  that  in  which  the  lens  is 
moved.  The  same  sort  of  motion  occurs  no  matter  in  which  direc- 
tion the  lens  is  moved,  whether  up  and  down  or  crosswise,  proving 
that  the  lens  is  a  spherical  one.  A  concave  spherical  lens  causes 
objects  seen  through  it  to  appear  to  move  with  the  lens,  that  is,  to 
the  right  when  the  lens  is  moved  to  the  right,  and  vice  versa.  See 
page  32  for  explanation.     To  ascertain  the  strength  of  the  sphere, 


take  a  spherical  lens  of  the  opposite  sign  from  the  trial  case,  of  about 
the  supposed  strength  of  the  spectacle  lens,  and,  holding  the  two  to- 
gether, move  them  from  side  to  side  and  from  above  downward.  If 
objects  seen  through  them  still  appear  to  move,  the  one  lens  does  not 
neutralize  the  other,  and  then  a  weaker  or  a  stronger  lens  is  selected 
from  the  trial  case  until  one  is  ascertained  which,  when  combined 
with  the  spectacle  lens,  allows  of  no  motion  in  objects  viewed  through 
them.  The  strength  of  the  lens  that  neutralizes  the  spectacle  lens 
is,  of  course,  known,  as  it  was  taken  from  the  trial  case.  The 
spectacle  lens  is  of  the  same  strength  but  of  opposite  sign  (contra- 
generic). 

Strong  contrageneric  spherical  lenses,  that  is  those  over  9  D.,  fail 
to  neutralize.  The  power  of  a  lens  depends  upon  its  index,  its  curves 
and  its  thickness.  The  thickness  of  the  lens  may  be  neglected  in 
concave  spherical  lenses  between  .25  and  20  D.  as  their  centers  can 
be  made  of  infinite  and  equal  thinness.     In  convex  lenses  there  is 


SPECTACLE,    NOSE-GLASS   FITTING,    MEASURING   LENSES.  453 

however  an  increasing  thickness  as  the  strength  of  the  lens  grows 
greater.  It  is  evident  that  the  radius  of  curvature  of  a  lens  of  a  given 
strength  must  be  different  when  the  thickness  is  considered  than 
when  it  is  not.  Two  lenses  of  the  same  curvature  but  of  different 
thickness  do  not  have  the  same  refractive  power.  The  lens  surface- 
measure  (shown  in  cut  on  page  457)  is  unreliable  in  convex  lenses 
over  8  D.  as  the  thickness  of  the  lens  constantly  enters  into  the  calcu- 
lation of  its  strength.  The  only  way  to  measure  strong  convex  lenses 
is  with  the  screen  and  graduated  bar.  When  we  prescribe  convex 
lenses  stronger  than  8  D.  we  should  remember  that  if  they  are  meas- 
ured by  neutralization  with  concave  lenses  they  are  always  weaker 
than  the  strength  of  the  concave  lens  would  indicate.  The  convex 
lenses  in  the  trial  cases  are  not  exactly  what  they  are  numbered. 
Every  lens  should  be  ground  as  thin  as  it  can  be  made. 

A  cylindrical  lens  is  known  by  the  fact  that  objects  looked  at 
through  the  lens  appear  to  move  unequally  when  the  lens  is  moved 
in  a  different  direction.  When  the  cylinder  is  moved  in  the  direction 
of  its  axis  there  is  no  apparent  movement  of  objects  seen  through  it, 
and  when  moved  in  a  direction  at  right  angles  to  that  there  is  decided 
motion  either  with  or  against  the  movement  of  the  lens  according  to 


its  sign.  If  the  cylinder  is  held  so  that  its  axis  is  oblique  then  objects 
appear  to  move  in  an  oblique  manner  when  the  lens  is  moved  verti- 
cally or  horizontally.     If  a  straight  line,  the  edge  of  the  door  or  win- 


454  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

dow  frame  or  what  not  be  looked  at  through  a  cylindrical  lens  with 
an  oblique  axis,  the  part  of  the  line  seen  through  the  cylinder  will  be 
inclined  to  the  right  or  to  the  left  according  to  the  position  of  the 
axis  of  the  cylinder  while  the  line  as  seen  above  through  and  below 
the  cylinder  will  appear  continuous  if  the  lens  has  a  vertical  or  hori" 
zontal  axis. 

The  inclination  of  the  axis  of  the  cylindrical  spectacle  lens  must 
first  of  all  be  ascertained.  This  can  be  done  with  a  protractor.  The 
protractor  is  a  circle  divided  into  degrees ;  at  the  center  is  a  figure 
the  shape  of  a  spectacle  lens,  upon  which  the  lens  to  be  tested  is  laid. 
An  ink  line  is  first  drawn  across  the  lens  coinciding  with  its  axis,  and 
then  laid  upon  the  protractor.  The  angle  at  which  the  ink  line  now 
stands  denotes  the  position  of  the  axis  of  the  cylinder  in  the  spectacle 
or  nose-glass  frames.  The  lens  is  laid  upon  the  protractor  with  the 
side  that  goes  next  to  the  eye  of  the  wearer  up.  Inasmuch  as  a 
line  looked  at  through  a  cylinder  with  oblique  axis  appears  broken 
and  can  be  made  to  appear  continuous  by  either  rotating  the  cylinder 
to  the  right  or  to  the  left,  so  that  the  axis  is  either  parallel  to  or  at 
right  angles  to  the  line  looked  at,  some  definite  plane  must  be  fol- 
lowed in  marking  the  axis^  of  a  cylinder. 

When  the  upper  end  of  a  line  seen  though  a  cylindrical  lens  is 
tilted  to  the  right,  rotate  the  lens  to  the  right  until  the  line  is  con- 
tinuous, then  mark  the  lens  parallel  to  the  observed  Hne.  This  line 
will  be  parallel  to  the  axis  of  the  cylinder  if  it  is  convex  and  at  right 
angles  to  it  if  concave.  When  the  portion  of  the  observed  line  seen 
through  the  cylinder  tilts  to  the  left,  rotate  the  lens  to  the  left,  until  the 
line  is  continuous,  and  then  mark  lens.  This  line  is  parallel  to  the 
axis  of  the  lens  if  convex,  and  at  right  angles  to  it  if  concave.  After 
the  axis  of  the  lens  has  been  determined  hold  the  lens  so  that  the 
axis  is  vertical,  and  then  move  up  and  down  and  crosswise.  If  the 
lens  is  a  plain  cylinder  there  will  be  motion  in  objects  when  the  lens 
is  moved  up  and  down,  and  the  motion  crosswise  will  indicate  the 
sign  of  the  cylinder.  Then  select  a  contrageneric  cylinder  from  the 
trial  case  of  lenses,  until  one  is  found  that  neutralizes  motion  in  ob- 


SPECTACLE,  NOSE-GLASS   FITTING.    MEASURING   LENSES.  455 

jects  seen  through  the  lens  when  the  latter  is  moved  from  side  to  side. 

The  axis  of  a  cylindrical  lens  can  also  be  readily  determined  in  the 
following  ingenious  manner :  From  the  center  of  the  draftman's  pro- 
tractor attach  a  thread  with  sealing  wax,  weight  the  end  of  the  thread 
with  a  bullet.  Place  the  spectacles  upon  the  upper  edge  of  the  pro- 
tractor with  the  lenses  occupying  the  position  they  do  upon  the  face. 
The  center  of  the  lens  to  be  measured  should  be  over  the  insertion 
of  the  thread.  A  vertical  line  is  then  sighted  through  the  lens  and 
the  latter  with  the  protractor  rotated  until  it  appears  continuous,  ro- 
tating to  the  right  if  the  upper  end  of  line  tilts  to  right  and  to  the 
left  if  the  upper  end  tilts  to  the  left.  The  weighted  thread  will  indi- 
cate upon  the  circumference  of  the  protractor  the  degree  of  inclina- 
tion of  the  axis  of  the  lens  if  convex  and  90  degrees  from  the  axis  if 
the  lens  is  concave. 

The  axis  of  a  cylinder  alone  or  in  combination  may  be  located  in 
the  following  manner :  Place  the  glasses  in  a  trial  frame,  with  the 
lenses  in  the  position  that  they  would  occupy  upon  the  face.  Sight 
a  straight  line  through  the  cylinder,  and  then  turn  the  cylinder  with 
the  trial  frame  so  that  the  line  seen  through  it  appears  upright. 
Now  place  a  contrageneric  cylinder  from  the  trial  case  in  front  of  the 
spectacle  lens,  of  proper  strength  to  neutrahze  the  latter.  The  incli- 
nation of  the  selected  cylinder  is  then  read  from  the  graduations  of 
the  trial  frame,  which  is  also  the  inclination  of  the  axis  of  the  cylinder 
in  the  spectacle  lens. 

A  sphero-cylindrical  combination  is  recognized  by  the  fact  that 
when  the  lens  is  neutralized  in  one  meridian  there  is  still  motion  of 
objects  seen  through  it  when  it  is  moved  at  right  angles  to  the  former 
direction.  We  first  ascertain  the  position  of  the  combined  cylinder 
as  outlined  above,  then  we  ascertain  the  nature  of  the  combinadon, 
whether  it  is  positive  or  negative,  by  moving  the  lens  parallel  to  and 
in  a  direction  at  right  angles  to  its  axis.  A  contrageneric  sphere  is 
then  selected  that  will  neutralize  modon  of  objects  in  direcdon  of  the 
axis  of  the  lens.  The  strength  of  this  sphere  indicates  the  strength 
of  the  sphere  in  the  combination.     A  cylinder  is  then  found  that  will 


456 


THE   EYE,    ITS   REFRACTION   AND    DISEASES. 


in  addition  neutralize  the  motion  of  objects  in  a  direction  at  right 
angles  to  the  axis  of  the  combination  spectacle  lens,  or  a  stronger 
sphere  may  be  selected  the  second  time,  and  then  the  difference 
between  the  strength  of  the  two  spheres  indicates  the  amount  of 
astigmatism. 

The  lenses  unless  otherwise  desired  should  be  properly  centered 
in  the  frames.  To  locate  the  optical  center  of  a  lens,  view  a  straight 
line  through  the  lens  and  move  the  lens  to  the  right  or  to  the  left 
until  the  portion  of  the  line  seen  through  the  lens  is  continuous  with 
that  seen  above  and  below  the  lens.  Draw  an  ink 
line  across  lens  over  the  Hne  seen  through  it.  Turn 
the  lens,  and  make  a  second  line  upon  it  in  the  same 
manner  at  right  angles  to  the  first.  The  two  diam- 
eters thus  constructed  will  cross  at  the  optical  center 
of  the  lens.  Or  one  may  view  crossed  lines  through 
the  lens  and  move  it  one  way  or  the  other  until  both 
arms  of  the  cross  seen  througrh  the  lens  are  con- 
tinuous  with  the  portion  of  the  arms  seen  above, 
below  and  to  either  side  of  the  lens. 

Prisms  or  prismatic  combinations  are  recognized 
by  the  fact  that  an  object  looked  at' through  them 
appears  to  describe  a  circle  when  the  lens  is  rotated 
about  its  center.  Objects  also  seen  through  them 
appear  displaced  in  space  in  the  direction  of  the 
apex  of  the  prism.  The  strength  of  the  prism  may 
be  ascertained  by  neutralizing  with  a  prism  from  the 
trial  case,  or  the  Dennet  prism  scale  may  be  used, 
which  is  designed  for  the  measurement  of  prisms  by 
any  of  the  units  thus  far  proposed.  It  gives  the  tangent  of  angular 
displacement  at  the  distance  designated  for  each  unit.  The  prism 
should  be  held  in  the  position  of  minimum  deviation.  The  scale  is 
hung  vertically  upon  the  wall,  and  the  prism  so  held  before  one  eye 
that  its  apex  intersects  the  pupil,  giving  rise  to  a  monocular  diplopia. 
The  origin  of  the  scale  is  then  seen  doubled,  the  distance  separating 


A 

ZT"  ■* 

^3—   5 

III  llljTTT 

0 

945. 


SPECTACLE,    NOSE-GLASS    FITTING,    MEASURING    LENSES. 


457 


the  doubled  images  of  the  prism  upon  the  scale  denoting  the  strength 
of  the  prism  tested  according  to  one  of  the  several  units  of  measure- 
ment depending  upon  the  distance  of  the  observer  from  the  scale. 

If  the  scale  is  regarded  with  one  eye,  and  the  prism  to  be  tested  is 
placed  before  the  other  one  as  is  usually  done,  producing  a  binocular 
diplopia,  any  muscular  inefficiency  of  the  observer  influences  the  cor- 
rectness of  the  test.  Within  certain  limits  one  can  measure  centrads 
and  prism-diopters  with  equal  accuracy.  To  do  this  it  is  necessary 
to  stand  at  five  meters.  To  measure  meter-angles  the  left-hand  num- 
bers are  to  be  used,  and  one  must  move  seven  centimeters  towards 
the  scale  for  every  millimeter  that  the  pupillary  distance  exceeds  60 
mm.,  and  ten  centimeters  further  away  from  the  scale  for  every  milli- 
meter that  it  falls  short  of  that  number.  To  measure  deviation  in 
degrees  it  is  necessary  to  hold  the  prism  three  quarters  of  a  meter 
further  back,  and  the  scale  reading  is  then  divided  by  two.  To 
measure  refracting  angles  it  is  necessary  to  be  at  5.28  m.  In  none 
of  the  cases  will  the  error  be  more  than  the  width  of  a  line.  To 
get  the  prismatic  power  of  a  strong  sphero-cylinder,  cover  it  with  a 
diaphragm,  having  a  central  aperture 
of  about  5  mm.  and  then  produce  in 
one  eye  diplopia  or  doubling  of  the 
scale  by  the  quick  passage  of  the 
lens  back  and  forth  before  the  eye. 
Lenses  over  5  D.  may  be  accurately 
measured  in  the  following  manner. 
To  the  origin  of  the  scale  a  very 
small  reflecting  surface  or  a  small  gas 
jet  is  fixed.  On  the  lens,  as  it  is 
passed  in  front  of  the  eye  as  above 
directed,  a  pin  is  so  held  that  its  point 
is  at  the  geometrical  center  of  the 
lens.  In  the  midst  of  the  diff"usion 
caused  by  the  point  of  light  will  be 
seen  the  imao^e  of  the  pin,  and  always  at  the  same  distance  from  the 


458 


THE   EYE,    ITS   REFRACTION   AND   DISEASES. 


origin,  which  is  easily  measured.  If  the  observer  wears  glasses  he 
should  remove  them  as  turning  the  head  and  looking  obliquely 
through  the  glasses  often  vitiates  the  experiment.  Instead  of  the  pin 
an  ink  dot  may  be  made  upon  the  lens.  With  two  such  lenses,  one 
minus  and  the  other  plus  of  at  least  5  D.,  all  spectacle  lenses  may  be 
examined.  There  are  a  number  of  appliances  upon  the  market  for 
the  measurement  of  lenses.  The  one  commonly  employed  is  shown 
in  the  cut. 

The  lens  is  pressed  upon  the  three  points  a,  b  and  c,  and  the  hand 
indicates  the  refracting  power.  It  can  be  used  for  spheres,  cylinders 
and  compound  lenses.  To  measure  the  refracting  angle  a  prism 
may  be  placed  between  the  legs  of  an  ordinary  pair  of  dividers,  so 
that  its  legs  fit  closely  along  its  two  sides  in  the  base-apex  direction. 
If  the  frame  of  the  glass  interferes  or  its  edge  is  cut  too  thin,  a  small 
coin  placed  upon  one  or  both  sides  of  the  prism  will  obviate  this 
difficulty.  The  number  of  degrees  are  then  read  off  by  placing  the 
dividers  upon  a  protractor  the  radius  of  which  is  equal  to  the  length 
of  the  legs  of  the  dividers.  If  the  prism  is  combined  with  a  lens,  the 
dividers  must  be  made  to  embrace  it  at  its  geometrical  center. 


Table  Showing  the  Deviation  Produced  by  the  Refracting  Angle'Series,  by  Centrads, 
BY  Prism-Diopters,  and  by  Meter-Angles. 


S.       s 

«              c 

a 

0 

efractii 
Angle, 

eviatio 

entrad 
eviatio 

Pr.  D. 
eviatio 

Meter 
Angle. 

eviatio 

pt:        » 

y           Q 

0 

Q 

c         0      1      u 

V            0        4       U 

^       0     /    // 

°»-      0    1     II 

I  =0  32  20 

1  =  0  34  22 

1=034  22 

1  =  143    6 

2=1      450 

2=1      845 

2  =  1      9 

2  =  3  26  12 

3  =  I  37  20 

3 -=143    7 

3  =  143 

3  =  5    918 

4  =  2    I  20 

4  =  2  1730 

4  =  2  17 

4  =  65224 

5  =  242    8 

5  =  251  53 

5  =  252 

5=830    5 

6  =  3  14  50 

6  =  3  26  15 

6  =  3  26 

Yox  p.d.  of  .06 

7  =  3  47  20 

7  =  4    038 

7  =  4 

8  =  4  20    2 

8  =  4  33  10 

8  =  4  34 

I  =  I  50 

9  =  45140 

9  =  5    923 

9  =  5  12 

2  =  3  40  43 

10  =  5  23  40 

»o  =  5  43  46 

»o  =  5  43 

3  =  5  30  41 

11=5  5820 

11=6  18    8 

II  =  6  17 

4  =  721  23 

12  =  632 

12  =  6533* 

12  =  6  51 

5  =  912    3 

>3  =  7    450 

13  =  92653 

13  =  724 

For />.(/.  of  .064 

14  =  7  38 

14  =  8    I  16 

14  =  758 

15  =  81132 

15  =  8  35  39 

15  =  832 

SPECTACLE.    NOSE-GLASS   FITTING,    MEASURING   LENSES.         459 

One  often  wishes  to  know  with  exactness  the  amount  of  prismatic 
effect  caused  by  decentering  a  lens  a  given  amount.  The  relations 
between  decentering  and  prismatic  action  are  easily  obtained  from 
the  properties  of  lenses.  Every  ray  passing  through  a  lens  makes 
an  angle  with  the  central  ray  passing  through  the  lens  after  refrac- 
tion, which  is  the  amount  of  deviation  produced  by  the  lens  at  that 
point.  The  tangent  of  this  angle  (between  central  and  refracted  ray) 
is  the  amount  of  decentering  of  the  lens,  the  focal  distance  of  the  lens 
being  the  radius.  Hence  if  D  represent  the  strength  of  the  lens  in 
diopters,  and  7  the  amount  of  decentering, /the  focal  distance  (equal 
to  I  //?),  and  d  the  amount  of  deviation,  we  have 

ylf=  tan  d,  or  Dy  =  tan  d. 

Multiplying  both  sides  of  this  equation  by  1 00  to  reduce  to  prism 
diopters,  100  Dy^d^.  The  same  formula  applies  to  centrads,  that 
is  100  Dy  =  d^.  For  degrees  reduce  by  the  coefficient  .57295, 
^'jDy  =  d°.     For  meter-angles  divide  by  3,  igDy  =  d^-. 

At  times  the  strength  of  two  prisms  combined  with  their  axes  not 
parallel  is  required.  The  problem  is  solved  by  spherical  trigonome- 
try, where  each  side  of  the  triangle  is  an  arc,  equal  in  degrees  to  the 
deviation,  and  where  one  of  the  angles — that  between  the  two 
prisms — is  given.     The  formula  is 

cos  a  =  cos  d  cos  c  —  sin  d  sin  c  cos  A,  ( i ) 

in  which  the  small  letters  represent  the  sides  and  the  large  ones 

angles.     The  following  example  will  illustrate.     What  is  the  result 

of  putting  before  the  eye  two 

prisms,  the  one  being  at  o"^  and 

the   other  at   35°    on   the   trial 

frame,    supposing   that    d  =  9** , 

c  =  5^',    and   a   the   strength   of 

the  resulting  prism?     Cos  ^  =  .9877  X  ,9962  —  .1564  X  .0871  X  ,8192 

=  ,97174,   which    is    the    cosine    of  the   resulting   prism,    13°   24'. 

The  customary  method  is  to  consider  this  question  one  in  simple 


46o  THE   EYE,    ITS   REFRACTION   AND   DISEASES. 

trigonometry,  using  the  formula  for  the  solution  of  oblique  triangles, 
changing  the  sign  of  the  cosine  as  before  because  the  angle  between 
the  two  prisms  becomes  the  angle  in  the  triangle  to  be  solved.  The 
formula  is  then 

a^  =  b^ -^  (^  -  2bc  co^  A.  (2) 

When  the  angle  A  between  the  two  prisms  is  90  degrees  the  last 
term  in  the  equation  becomes  o.  The  problem  is  then  reduced  to 
the  proposition  of  Pythagoras,  namely — that  the  resultant  prism  is 
the  square  root  of  the  sum  of  the  squares  of  the  other  two  prisms. 

The  strength  of  the  prisms  being  given,  either  of  the  angles  can  be 
found  by  the  formula 

cos  ^  =  —  +  —  —■ — ,  (3) 

2ac      2ac      2ac  ^  ' 

or  when  A  is  a.  right  angle, 

tan  ^  =  c/d. 

If  one  prism  is  placed  before  each  eye,  the  sign  of  the  last  term  of 
the  equation  No.  2  is  to  be  changed  from  minus  to  plus,  and  the  last 
term  of  equation  No.  3,  from  plus  to  minus,  or  add  180°  to  the  posi- 
tion of  the  prism  in  the  trial  frame  and  the  formulae  are  used  as  they 
are  written  above. 

Suppose  we  wish  to  know  how  to  insert  a  lens  in  the  frame,  with- 
out taking  the  trouble  to  focus  or  measure  it.  It  will  be  recalled 
that  the  strongest  convex  or  the  weakest  concave  curve  is  to  be 
placed  in  the  frame  away  from  the  eye.  If  we  know  which  surface 
of  the  lens  goes  from  the  eye  the  inclination  of  the  combined  cylinder 
will  be  right.  To  decide  which  is  the  plane,  curved  or  cylindrical 
surface  of  the  lens  we  view  the  reflection  of  some  distant  object  from 
its  surfaces.  Suppose  the  lens  is  a  i  D.  C.  ax.  30.  On  one  side  of 
the  lens  we  can  easily  get  the  reflection  of  some  distant  object ;  we 
can  turn  the  lens  with  either  its  short  or  long  diameter  at  right  angles 
to  the  eye  and  still  the  distinctness  of  the  reflection  will  not  be  inter- 
fered with.     But,  if  we  turn  the  other  side  of  the  lens  up,  and  use  it 


SPECTACLE,    NOSE-GLASS   FITTING,    MEASURING   LENSES.         46 1 

as  a  reflector,  we  will  find  that  there  is  only  one  direction  in  which 
we  can  obtain  a  distinct  reflection,  and  as  we  turn  the  lens  the  image 
becomes  distorted.  Therefore  this  surface  is  the  cylindrical  one,  and 
as  this  surface  in  this  case  is  to  go  out  or  away  from  the  eye  we  screw 
the  lens  in  the  frame  so  that  the  long  axis  of  the  lens  is  horizontal 
and  if  the  lens  is  ground  correctly  the  axis  of  the  cylinder  will  have 
the  proper  inclinadon.  It  makes  no  difference  which  edge  goes 
towards  the  nose  or  temple  side,  so  long  as  the  cylindrical  surface  is 
kept  away  from  the  eye.  Again  take  as  example  a  lens  of  +  i  D.S. 
wl+  I  D.C.  ax.  90.  On  sighting  across  this  lens  as  before  we  will 
find  that  on  one  surface  we  get  a  more  or  less  distorted  image, 
which  is  equally  so  no  matter  which  way  the  lens  is  turned.  This 
then  is  the  spherical  surface.  If  we  now  look  on  the  opposite  side 
of  the  lens  we  will  find  that  there  is  only  one  position  in  which  we 
can  obtain  a  distinct  image,  and  as  the  lens  is  rotated  it  becomes 
much  distorted,  hence  this  is  the  cylindrical  side  which  in  this  case  goes 
towards  the  eye.  Suppose  again  that  we  have  a  lens  of  —  ^wf—  i 
ax.  165°. 

We  will  find  as  before  that  one  side  gives  a  more  or  less  altered 
or  distorted  image  in  all  directions,  and  that  the  other  surface  gives  a 
distinct  reflection  in  one  direction  and  a  distorted  one  in  every  other. 
As  the  strongest  concave  side  goes  towards  the  eye,  the  cylinder 
will  go  out. 


APPENDIX. 


The  following  formulae  are  those  commonly  employed  in  optics. 
The  deduction  of  each  will  be  found  in  the  text  of  the  book. 


$^  =  -^.    (Snell's  Law)  (page  7) 


F= 


2 
R 


V 


V 


F= 


—  I 


R 


00 

(25) 
(25) 


F 


d      I 

D-^O-  (30) 

^  =  -^  -  ^  (for  convex).      (31) 


Z>d?=  i^F (Newton's  Formula).   (53) 

(53) 
F      F 


2~^  "^  P)  ^^^^  concave). 

(31) 

2 

(52) 

I            I           I 

7+77  =  ^. 

(52) 

I           I           I 

f'-'p-J' 

(53) 

0      D      F 
I~F~d' 

(53) 

J  =  2DR. 


I  I  I 


I    I 

F= 


I 
F 


ID 


0 


V 


R 


CC  =  F'F". 


y'= 


F'F' 
-•  1  -*  2 


piip" 
-*  1  -*  2 


F'F' 

d  ' 

pnpn 

F'IF^=  V'jV' 


(53) 

(53) 

(53) 

(54) 

(64) 

(65) 
(66) 

(67) 

{^7) 

(67) 

(72) 


462 


0=  2  tan  2.5°- A 

d 
^  d-\-  a 

A=p-R  =  D-S. 


F" 


APPENDIX, 
(8i) 
(88) 

(90) 
(104) 

(127) 

(244) 


463 


c  _  b  —  [F"  —  F')       F" 
d^ 


As^  =  k+p-As^.         (391) 

D    •  (395) 

F  >^F' 


R=^-l 


0'  = 


C 


f"  =  l±C". 


(436) 

(439) 


INDEX. 


Abduction,  205,  423 
Aberration, 

Chromatic,  15 

Of  eye,  38,  39 
Test,  326 

Spherical,  34,  35 
Aberroscope,  40,  10 1 
Accommodation,  58,  86,  260,  275 

Amplitude  of,  87,  89 

Exophoria  in,  306 

Helmholtz  theory  of,  98 

Influence  of  age  on,  304 

Mechanism  of,  94 

Relative,  104,  105 

Tscherning's  theory  of,  98,  100 
Achromatopsia,  165 
Adaptation,  period  of,  270 
Adduction,  205,  423 
Amblyopia,  273 

Exanopsia,  273 

Acquired,  273 

Congenital,  273 

Meridional,  302 
Ametrometer,  Thompson's,  322 
Ametropia,  324 
Anaphoria,  265,  424 

Test  for,  424 
Angle, 

Alpha,  106,  398 

Beta,  106 

Gamma,  106 

Kappa,  106 

Critical,  11 


30 


Angle, 

Of  deviation,  10 

Of  incidence,  5 

Of  refraction,  5 

Of  reflection,  47,  48 

Refracting,  11 

Meter,  102 

Visual,  77,  79 

Limit  visual,  79 
Anisometropia,  257 
Aphoses,  197 
Aphakia,  435 

Apparatus,  divisions  of  visual,  154 
Artery, 

Retinal,  135 

Cilio-retinal,  136 
Asthenia,  ciliary,  262 

Treatment  of,  262,  263 
Astigmatism,  241,  253,  288 

Against    the    rule   (indirect),    242, 

295 
Band  appearance  in,  365,  366,  367, 

369 
By  incidence,  242,  252 

Causes  of,  241 
Compound,  242 
Correction  of  irregular,  255 
Diffusion  in,  244 
Focal  lines  of,  243,  244 
Horizontal,  242 
Irregular,  242,  252 
Latent,  283 
Manner  of  detecting,  254 


465 


466 


INDEX. 


Astigmatism,  Mixed,  296 

Mixed,  in  retinoscopy,  365 

Oblique,  242 

Ophthalmometric,  391 

Principal  meridians  of,  2 

Physiological,  269 
.    Regular,  242 

Retinoscopy  in,  365 

Simple,  242 

Stenopaic  slit  in,  299 

Supplementary,  391 

Symptoms  of,  248,  249 

Tests  for,  280,  287,292  ; 

To  exclude  effect  of,  278  ^ 

Treatment  of,  250,  251 

Varieties  of,  247,  256,  257 

Vertical,  242 
Astigmometer,  Hotz',  329,  372 
Axis  or  axes, 

Corneal,  106 

Listing's,  214,  215 

Optic,  106 

Primary  ocular,  203 

Secondary  ocular,  205 

Visual,  106 
Axonometer,  367 
Bands,  interference,  3 

Of  light  in  astigmatism,  365,  366, 

367,  369 
Blind  spot, 

Mariotte's,  149 

Filling  in  of,  185 

Demonstration  of,  185 
Bodies,  Bowditch's,  196 
Cabinet,  ophthalmic,  276 

Cards,  Astigmatic,  279 
Green's,  280 
Hill's,  281 
Pray's,  281 


Carus,  Verhoffs,  282 
Cataphoria,  265,  424 
Centers,  primary  optical,  160 
Center,  visual,  194 

Of  rotation,  203 
Chromoscope,  328 

Circle  of  diffusion,  36,  83,  90,  226,  261, 
274 

Size  of,  88 

Listing's  table  of  size  of,  88 
Clinometer,  222 

Clinoscope,  218  J 

Color-blindness,  165 
Colors, 

Complementary,  162,  163 

Hue,  162 

Intensite,   162 

Tint,  162 

Mixing  of,  in  the  eye,  161,  162 
Colored  pigment,  163 

Preference  for,  170 

Theories  of  perception,  162,  163, 164 
Contrast,  183 

Simultaneous,  P84 

Successive,  185 
Convergence,  loi 

Amplitude  of,  103 

In  myopia,  287 

Manner  of  estimating,  102,  103 

Relative,  104 

Unit  of  measure  of,  loi 
Cross-eyes,  203 
Crossed  cylinders,  301 
Cyclophoria,  265,  428 
Cycloplegics,  458 

Daltonism,  165 

Seebeck  or  Holmgren  test  for,  167 
Stilling' s  test  for,  167 
Test  with  spectroscope,  167 


INDEX. 


467 


Daltonism,  Lantern  test  for,  168 

Meyer's  test  for,  169 

Bonder's,  167 

Weber's,  167 

Wollfberg's,  167 
Deorsumduction,  205,  423 
Dichromasia,  169 
Diplopia,  141 

Physiological,  194 
Disc,  Stenopaic,  273 

Use  of  pin-hole,  274 

Placido's,  382 

Optic,  134 
Displacement,  parallactic,  121,  138 
Dyschromatopsia,  167 

Emmetropia,  58,  224 
Entoscope,  199 
Esophoria,  265,  410,  413 
Euphthalmin,  271 
Examination,  routine  of,  272 
Exophoria,  265,  410,  413 
Experiment  of  Young,  2 

Of  Wollaston,  38 

Of  Fechner,  173 

Of  Hering,  209 

Of  Javal,  217 

Of  Meissner,  216 

OfScheiner,  320 

Of  Volcker,  95 

Of  Volkmann,  217 
Eye,  schematic,  75 

Of  Helmholtz,  76 

Donder's  reduced,  77 

Listing's  reduced,   77 

Skiascopic,  376 
Eyeball,  cardinal  points  of,  105,  106 

Catoptric  images  of,  99 

Centers  of  s\u"faces  of,  400 

Dioptric  surfaces  of,  59 


Eyeball,  Gross  anatomy  of,  56,  57 

Measurements  of,  56 

Movements  of,  203 

Optical  defects  of,  105,  106 
System  of,  71,  72,  73 

Radii  of  surfaces  of,  402 

Refraction  of,  59 
'unics  of,  56 
Eye  ground,  color  of,  1 33 

Appearance  of,  134,  135 
Eye  Strain,  224,  225 

Causes  of,  224,  225 

Symptoms  of,  225 

Field,  hemianopic,  149 

Ophthalmoscopic,  122,  123 

Struggle  of  the  two,  193 
Fixation,  binocular  field  of,  212,  213 

Field  of,  210,  211 

Line  of,  106 
Focus  or  foci. 

Of  concave  nurrors,  50 

Of  convex  mirrors,  53 

Of  cylindrical  lenses,  41 

Principal  focus  of  con  vex  lens,  20,  2  a 

Real,  21 

Secondary,  20,  21 

Virtual,  21 
Fundus,  tessellated,  138 

Color  of,  133 

Appearance  of,  134,  135 

Hemeralopia,  171 
Hemiablepsia,  159 
Hemianopia,  159 
Hemianopsia,  temporal,  159 

In  lesions  of  optical  centers,  160 

Inferior,  159 

Superior,  159 

Lateral  (homonymous),  159 


468 


INDEX. 


Heterophoria,  264,  406,  411 

Asthenic,  265 

Causes  of,  266 

Reversed,  265,  429 

Steven's  test  for,  418 

Sthenic,  265 
Hyperphoria,  265 
Hyperopia,  59,  226,  278 

Absolute,  229 

Consequences  of,  226,  227,  230 

Correction  of,  226,  278,  285 

Facultative,  229 

Latent,  229 

Manifest,  229 

Total,  229 

Treatment  of,  231 

Table  of  axial,  239 

Varieties  of,  228 

Illumination,  oblique,  131 

By  direct  sunlight,  132 
Illusions,  optical,  183,  187 
Images,  after,  175 

By  concave  spheres,  30 

By  convex  spheres,  26,  27,  28,  29,30 

By  concave  mirrors,  50,  51,52 

By  convex  mirrors,  53 

By  plane  mirrors,  48 

Of  Purkinje,  98,  379,  380 

Projection    of  in    ophthalmoscopy, 
124,  125 

Suppression  of  retinal,  142 
Impressions,  visual,  183 
Index,  refraction. 

Of  crown  glass,  7 

Of  flint  glass,  7 

Of  aqueous  humor,  7 

Of  cornea,  7 

Of  crystalline  lens,  7 

Of  vitreous  humor,  7 


Index,  of  water,  7 
Interval, 

Astigmatic,  of  Sturm,  243 
Iris,  apparent,  75 
Irradiation,  183 

Kinescopy,  325 
Keratoscopy,  344 

Law,  Fechner's,  172 

Listing's,  214,  216 

Snell's,  6,  7 
Lamina  cribrosa,  134 
Lens,  achromatic,  38 

Aperture  of,  34 

Concave  spherical,  C2 

Cylindrical,  16,  40,  453 

Cylindro-toric,  45 

Definition  of,  16 

Focal  plane  of,  1 7 
Interval  of,  18 

Focus  of  convex,  1 7 

Numeration  of,  18,  23 

Optical  center  of^  1 7 

Periscopic,  34 

Poles  of,  1 7 

Principal  axis  of,  1 7 

Secondary  axes  of,  1 7 
Focus  of,  20 

Spherical,  16 

Sphero-cylindrical,  43,  254,455 

Sphero-toric,  45 

Toric,  44 

To  ascertain  strength  of,  32 
Letters,  Snellen's,  80 

Standard,  81 

Test,  81 
Lens  measure,  457 
Light,  I 

Beam  of,  4 


INDEX. 


469 


Light,  Corpuscular  theory  of,  i 

Electro-magnetic  theory  of,  3 

Intensity  of,  i 

Immediate  source  of,  348 

Number  of  waves  of,  14,  15 

Original  source  of,  348 

Refraction  of,  4,  47 

Ray  of,  4 

Pencil  of,  4 

Propagation  of,  2 

Spectrum  of,  14,  16 

Undulatory  theory  of,  i 

Velocity  of,  i 
Light-shade,  Thorington's,  347 

Macula  lutea,  136,  137 

Projection  of,  193 
Malignering,  177 

Tests  to  detect,  178,  179,  180,  181 
Measure,  Frame,   448 
Medium  dioptric,  4 
Maddox  groove,  411 

Rod,  411 
Mirror,  definition  of,  47 

Concave,  49 

Conjugate  foci,  53,  54 

Convex,  49,  53 

Focal  interval  of,  52 

Plane,  48 

Principal  focus  of,  50 
Axis  of,  49 

Radius  of  curvature  of,  49 

Spherical,  49 

Vertex  of,  49 
Monoscopter,  212 
Muscle  or  muscles. 

Action  of  extra-ocular,  205 

Balance  of  extra-ocular,  264 

Imbalance  of  extra-ocular,  264 

Briicke's,  96 


Muscle  or  muscles,  Miiller's,  96 

Inefficiency  of  extra-ocular,  264 

Insufficiency  of  extra-ocular,  264 
Of  oblique,  421 
Myopia,  59,  231 

Cause  of,  232,  233 

Correction  of,  232,  285 

Malignant,  233 

Symptoms  of,  234,  235 

Table  of  axial,  240 

Treatment  of,  236,  237 

Varieties  of,  235 

Nerve,  anatomy  of  optic,  157 
Nose-glass  fitting,  448 

Object,  apparent  distance  of,  186 

Size  of,  186 
Opacities  in  dioptric  media,  131 
Ophthalmometer,  hand,  382 

Of  Javal  and  Schiotz,  383 

Manner  of  using,  386 
Ophthalmometry,  379 

Basis  of,  394 

Primary  position  in,  386 

Secondary  position  in,  387 
Ophthalmophakometer,  397 
Ophthalmo-dynamometer,  90,  91 
Ophthalmoscope,  107 

Invention  of,  107 

Knauer's,  113 

Loring's,  iii 

Morton's,  no,  115 

Refraction,  109 

Roth's,  114 

Simple,  109 
Ophthalmoscopy,  direct,  no,  112,  118, 

331 
In  hyperopia,  333 

In  myopia,  337 


470 


INDEX. 


Op thalmoscopy, Indirect,  no,  112,  340- 

343 

Auto-,  118,  128,  129 

By  sunlight,  129 

Magnification  by,  124,  126,  127 
Ophthalmo-cromoscopy,  1 30 
Ophthalmo-spectroscope,  130 
Optometers,  308 

Javal -Bull's,  308 

Coccius's,  314 

DeZeng's,  309 

Bonder's,  314 

Rod,  304,  314 

Sous' s,  314 

Young's,  40 
Orthophoria,  264 

Spasmodic,  429 
Orientation,  139 

False,  141 

Objective,  140 

Subjective,  141 

Perimeter,  144 

Dana's,  14^ 

Meyrowitz's,  146 

Skeel's,  147 

Hardy's,  147 
Phoses,  196 
Phenomenon,  Bell's,  210 

Troxler's,  176,  209 
Phenomena,  entoptic,  195-202 
Phorometer,  Stevens's,  414 
Phoroscope,  Aiken's,  411 
Phosphenes,  186 
Photometer,  Forster's,  172 
Planes,  cardinal,  60 
Points,  cardinal,  60 

Properties  of  cardinal,  61 

Method  of  locating  cardinal,  66 

Of  crystalline  lens,  69,  70,  71 


Points,Of  schematic  eye,  77,  78 
Point,  Bonder's  presbyopic  point,  304 

Of  reversal,  351,  365 
Porus  opticus,  135 
Position,  primary,  206 

Secondary,  206 
Prisoptometry,  323 
Prism, 

Achromatic,  15 

Apex  of,  9 

Base  of,  9 

Befinition  of,  9 

Bispersion  of,  15 

Position  of,  9 

Minimum  deviation,  of,  10 

Numeration  of,  12,  13 

Refraction  through,  9 
Angle  of,  9 

Risley's,  413 

Maddox,  16 
Presbyopia,  97,  224,  260 

Correction  of,  262,  302 

BeSchweinitz's  method  in,  305 

Symptoms,  261     , 
Projection  of  object,  140 
Pupil,  apparent  size  of,  74 

Apparent  position  of,  75 

Apparent,  75 

Of  entrance  and  exit,  75 
Pupillometer,  443 
Puncture  proximum  (p"),  87 

In  E.  H.  &  M.,  90-93 

Remotum  (R),  87 

In  E.  H.  &  M.,  90-93 

Rays  of  light,  4 
Harmful,  379 
Homocentric,  60 
Incident,  4 
Lost,  379 


INDEX 


471 


Rays  of  light,  Refracted,  4 

Reflected,  47 

Useful,  379 

Ultra,  161 
Redress,  movement  of,  407 
Reflections  in  ophthalmoscopy,  130,  131 

Internal,  11 

Total,  II 
Reflex,  foveal,  137 

Macular,  137 

Chorioidal,  no 
Refraction,  normal,  224 

Absolute  index  of,  6 

Caustics  by,  35,  55 

Demonstration  of,  7,  8 

Dynamic,  87 

Error  of,  224 

Explanation  of,  5,  6 

Index  of,  6 

Limit  angle  of,  1 1 

Static,  86 

Total,  II 

To  exclude  error  of,  278 

To  deduce,  of  complete  eye  from 
that  of  aphakic  eye,  440 
Refractometer,  Lambert's,  357 
Retinoscope,  345 

Fuller's,  371 
Retino-skiameter  (Cross),  359,  360 
Retinoscopy,  344 

Apparent  movement  in,  348 

Description  of,  348 

Form  of  light  area  in,  353 
Magnification  of  retina  in,  351 
Mixed  astigmatism  in,  372 
Measurement  of  accommodation  by, 

375 
Real  movement  of  light  in,  348 
Leroy's  explanation  of,  354  I 

Paracentral  shadow  in,  368  I 


Retinoscopy,  Practical  application  of,  356 
Spherical  aberration  in,  369 

Ridgeway's  test,  327 

Rotation,  centers  of,  203 
Axes  of,  205 

Scale,  prism,  456 
Simulated  blindness. 

See  malignering 
Scotomata,  149 

Absolute,  149 

Annular,  149 

Central,  149 

Fixed,  149 

Motile,  149 

Negative,  149,  151 

Peripheral,  149 

Positive,  149,  151 

Relative, 
Sensation  guiding,  264 
Sense,  color,  139,  161 

Form,  139 

Light,  139,  171 
Acuity  of,  174 
Shadow  Test,  334 
Skiascopy,  344 
Skiascopes,  356 
Spectacle  fitting,  443 
Spectra,  ocular,  186 
Spot,  Mariotte's  blind,  149 

Measurement  of  blind,  153 
Size  of,  153 
Stenopaic  slit,  299 

Manner  of  using,  299 
Streak,  reflex,  135 
Cause  of,  135 
Surface,  dioptric,  4 
Sursumduction,  205,  423 
Squint,  265,  273 
Dynamic,  265 


472 


INDEX. 


Sqmnt,  Latent,  265 

Caused  by  myopia,  265 

Table  of  cycloplegics,  270 

Prismatic  deviation,  458 

Torsion,  222 
Test,  fogging,  269,  282,  283,  296 

Von  Graefe's  screen,  407,  408 

Parallax,  407 
Test,  Cards, 

Brackets  for,  277 

Forster's,  275 

Guillery's,  85 

Jaeger's,  85 

Javal's,  85 

Snellen's,  85 

Randall's,  81 

Reversed,  275 

Landolt's,  81 

Williams',  84 

Ziegler's,  85 

For  near  vision,  85 
Threshold,  the,  174 
Theory  of  parent,  the,  354 
Trial  case,  271 

Plan  of  Procedure  with,  271 


Tropometer,  207 

Directions  for  using,  208 

Vein,  retinal,  136 
Vision,  acuteness  of,  80 

Absolute  field  of,  149 

Binocular  field  of,  153 

Central,  139 

Curtailment  of  field  of,  149 

Estimation  of  field  of,  86 

Extent  of  field  of,  147 

Evidences    gained    from     field    of, 
278 

Field  of,  142,  152 

In   optic   nerve  diseases,   156, 

157 
Chiasm  diseases,  158,  159 
Tract  diseases,  159 
Diseases    of    optical    centers, 
160 
Manner  of  expressing  acuity  of,  82, 

84 
Overshot  field  of,  159 
Peripheral,  139 
Relative  field  of,  149 
Stereoscopic,  141,  191 


THE  REFRACTION  OF  THE  EYE 

INCLUDING   A   COMPLETE  TREATISE   ON   OPHTHALMOMETRY  ;    A 
CLINICAL  TEXT-BOOK   FOR   STUDENTS  AND  PRACTITIONERS 

By  A.  EDWARD  DAVIS,  AM^  M.D. 

Cloth.     8vo.     $3.00  net.     With  119  Engravings,  97  of  which  are  original 


The  author  outlines  a  routine  method  of  examination  to  be  followed  in  every  case. 
Each  step  of  the  examination  that  is  necessary  to  be  made  in  fitting  a  patient  with  glasses 
is  described  in  detail.  With  the  use  of  the  ophthalmometer  to  detect  the  corneal  astigma- 
tism, and  by  following  this  routine  method  of  examination,  spasm  of  accommodation,  if 
present,  can,  in  the  great  majority  of  cases,  be  overcome,  and  if  not  present,  the  liability 
of  causing  it  avoided.  Thus  the  use  of  a  mydriatic  is  rendered  unnecessary,  except  on 
rare  occasions — in  not  more  than  one  per  cent,  of  all  cases  of  errors  of  refraction. 

The  entire  subject  of  the  refraction  of  the  eye  is  treated  in  this  volume.  A  feature  of 
the  book  is  a  report  in  full  of  one  hundred  and  fifty  clinical  cases,  illustrating  practical 
points  in  the  fitting  of  glasses  and  in  the  use  of  the  ophthalmometer.  Many  diagrams  are 
used  to  show  the  focus  of  the  principal  meridians  of  the  eyes,  so  that  the  merest  tyro  must 
understand  them. 

The  most  complete  and  detailed  description  of  the  ophthalmometer,  together  with 
concise  and  definite  rules  for  its  use,  are  given.  These  rules  contain  the  best  practical 
directions  for  using  the  instrument  accurately,  and  by  their  aid  alone  the  careful  student 
will  learn  to  use  the  instrument  correctly. 


THE  OPHTHALMIC  PATIENT 

A   MANUAL.  OF  THERAPEUTICS   AND   NURSING   IN   EYE   DISEASE 

By  PERCY  FRIDENBERG,  M.D. 

ophthalmic  Surgeon  to  the  Randall's  Island  and  Infants'  Hospital,  Assistant  Surgeon  New  York 

Eye  and  Ear  Infirmary 

Cloth.     l6mo.     $1.00  net 


"  The  author  aims  to  explain  the  principles  and  to  describe  the  various  procedures  and 
appHances  of  ophthalmic  nursing,  the  technique  of  operative  assistance,  and  the  nature  and 
use  of  ocular  remedies,  as  exemphfied  in  private  practice  as  well  as  in  the  established 
routine  of  well-equipped  institutions.  The  book  is  intended  to  serve  as  a  practical  guide 
to  physicians,  students,  and  nurses  who  lack  special  training  in  the  care  of  ophthalmic 
cases,  as  well  as  to  supplement  the  invaluable  routine  of  the  ward  and  the  training-school 
with  theoretical  instruction.  The  author  has  thought  it  advisable  to  lay  most  stress  on 
actual  nursing,  and  to  treat  of  the  topics  of  pathology,  symptomatology,  and  diagnosis  only 
in  so  far  as  it  was  necessary  to  elucidate  his  own  theme,  for  this  volume  is  in  no  way  a 
treatise  on  diseases  of  the  Eye." — From  the  preface. 


--     .^T     ^^..^...Tmr      66  FIFTH  AVENUE, 

THE  MACMILLAN  COMPANY,       new  york 


DEFECTIVE  EYESIGHT 

THE  PRINCIPLES  OF  ITS  RELIEF  BY  GLASSES 

By  D.  B.  ST,  JOHN  ROOSA,  IVLD^  LL.D. 

Cloth.     l6mo.     $1.00  net 


This  treatise  takes  up  all  conditions  requiring  the  use  of  glasses,  and  indicates  in  the 
most  careful  manner  the  indications  and  rules  for  describing  them.  It  is  well  known  that 
the  author  is  a  conservative  in  regard  to  the  value  of  glasses,  believing  that  there  is  a 
limitation  to  their  use,  and  that  they  ought  not  to  be  prescribed  unless  of  positive  value. 
No  pains  have  been  spared  to  make  the  manual  a  complete  guide  to  the  practitioner  who 
wishes  to  understand  and  practice  the  rules  for  the  prescription  of  lenses  for  the  improve- 
ment of  impaired  sight.  The  book  may  also  be  interesting  to  educated  men  in  all  depart- 
ments of  life,  who  desire  to  be  informed  as  to  advances  that  have  been  made  in  this 
interesting  subject,  one  which  concerns  such  a  large  proportion  of  the  human  race. 


HANDBOOK  OF  OPTICS  FOR 
STUDENTS  OF  OPHTHALMOLOGY 

By  WILLIAM  NORWCX)D  SUTER,  B.A^  KLD. 
Cloth.    l6mo.    $1.00  net 


"  Simphcity  has  been  sought  so  far  as  this  is  not  incompatible  with  thoroughness. 
But  the  demonstrations,  some  of  which  may  appear  formidable  to  the  student,  require  no 
knowledge  of  mathematics  beyond  that  of  simple  algebraic  equations  and  the  elementary 
truths  of  geometry.  For  those  who  may  not  be  familiar  with  the  trigonometrical  ratios,  a 
brief  synopsis  has  been  furnished  in  an  appendix." — From  the  preface. 


THE  MACMIUUAIN  COMPAINY 

66  FIFTH  AVENUE  NEW  YORK 


V 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 

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